Calcul
Limites, dérivées, optimisation et comportement des fonctions.
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problem 14. (1 point) let ( f ) be a differentiable function. suppose t…
\(162\)
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let ( f ) be a twice - differentiable function with first derivative ( …
B. \(5xf(x^{2})-\int 5f(x^{2})dx\)
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differentiate. y = 2x² cos x cot x y =
\(4x\cos x\cot x - 2x^{2}\cos x-2x^{2}\cos x\csc^{2}x\) (or equivalent simplified forms)
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f(x) = -(x + 2)(x - 2)^2(x - 7) plot the y-intercept and the roots. cli…
Roots (x-intercepts): $(-2, 0)$, $(2, 0)$, $(7, 0)$ y-intercept: $(0, 56)$
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find $f(x)$ and $f(x)$ if $f(x) = \\frac{x^2}{x - 3}$. $f(x) = \\square…
\( f'(x)=\frac{x^2 - 6x}{(x - 3)^2} \) \( f''(x)=\frac{18}{(x - 3)^3} \)
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write a function in any form that would match the graph shown below.
$y=-\frac{1}{2}(x+1)(x-4)^2$ (or expanded form $y=-\frac{1}{2}x^3+\frac{7}{2}x^2-4x-8$)
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write a function in any form that would match the graph shown below.
$y=-\frac{1}{5}(x+5)^2(x-1)$
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9. 0 / 1 points let $h(x) = \\frac{f(x)}{1 + g(x)}$. given $f(5) = 1$, …
\( -\frac{1}{4} \)
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write a function in any form that would match the graph shown below.
$y=(x+3)(x-8)$ (or $y=x^2-5x-24$)
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7. 0 / 0.62 points practice another differentiate. \\( y = 4x^2 \\sin x…
\( y' = 8x\sin x\tan x + 4x^2\sin x + 4x^2\sin x\sec^2 x \) (or equivalent simplified forms, e.g., \( y' = 8x\sin x\tan x + 4x^2\sin x(1 + \sec^2 x) \) or further simplified using…
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for each of the following integrals, select the best method to evaluate…
s: 1. For \( \int\frac{3^{(\ln(x))^2}}{x}dx \), the best method is \( \boldsymbol{u} \) - substitution (let \( u = (\ln x)^2 \) or \( u=\ln x \) depending on the intended problem,…
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trazar el gráfico de la recta. -2x + y = -6
To graph the line \(-2x + y=-6\) (or \(y = 2x-6\)): 1. Plot the y - intercept \((0,-6)\). 2. Plot the x - intercept \((3,0)\) (found by setting \(y = 0\) in \(y = 2x-6\) and solvi…
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the solutions to the inequality $y > -3x + 2$ are shaded on the graph. …
B. (2, 0)
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las funciones f y g se definen a continuación. $f(x)=4x - 3$ $g(x)=-4x^…
\( f(-3) = -15 \) \( g(4) = -67 \)
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las funciones f y g se definen a continuación. $f(x) = -3x^3 - 2$ $g(x)…
\( f(-2) = \boldsymbol{22} \) \( g(7) = \boldsymbol{-17} \)
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problem 1. (1 point) for each of the following integrals, select the be…
1. D. $u = \sec(x)$ 2. C. $u=\tan(x)$
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question 29 find the derivative of $y = \\sin(3x^2 - 4x + 1)$. \\(\\fra…
$\frac{dy}{dx}=(6x-4)\cos(3x^2-4x+1)$
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question 28 consider the function $f(x)=\\sqrt3{x}$ near $x = 8$. find …
0.00008
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all sides of a square are increasing at a rate of 4 centimeters per sec…
$\boldsymbol{\frac{dA}{dt} = 80\frac{\text{cm}^2}{\text{sec}}}$ (corresponding to the second option)
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question 24 let ( f(x) = (12x^2 + 36)^5 ). find the differential, ( df …
$df = 120x(12x^2+36)^4dx$ (the fourth option)
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question 23 use the limit definition of the derivative to find $f(x)$ w…
$f'(x)=14x$
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question 22 write the equation of the line tangent to $f(x)=\\frac{1}{x…
y = -5x + 6
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467\ x36\ \ \ +\ \
Los números para los recuadros son: Primera fila: 2 8 0 2 Segunda fila: 1 4 0 1 Resultado final: $16812$
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question 19 find the derivative of $y = \\arctan(5x^2 - 1)$. \\(\\bolds…
$\boldsymbol{\frac{dy}{dx} = \frac{10x}{25x^4 - 10x^2 + 2}}$ (the third option)
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find the derivative of $f(x) = \\frac{1}{(2x^5 + \\sin x)^3}$.\ \ $\\bi…
$\boldsymbol{f'(x)=\frac{-3(10x^{4}+\cos x)}{(2x^{5}+\sin x)^{4}}}$ (the third option)
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trazar la recta. y=\\frac{1}{4}x+5
To draw the line \(y=\frac{1}{4}x + 5\), plot the y - intercept \((0,5)\) and use the slope \(\frac{1}{4}\) to find another point (e.g., \((4,6)\) or \((-4,4)\)) and draw a straig…
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question 17 find the derivative of $y = e^{5x}\\cos(3x)$. \\(\\frac{dy}…
$\boldsymbol{\frac{dy}{dx}=5e^{5x}\cos(3x)-3e^{5x}\sin(3x)}$ (corresponding to the third option)
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question 15 find the linear approximation of $f(x)=\\sqrt5{x}$ when $x …
L(x) = -1 + $\frac{1}{5}$(x+1)
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question 14 find the derivative of $f(x) = 3x^5\\sin x + 8\\cos x$. \\(…
$f'(x)=15x^{4}\sin x + 3x^{5}\cos x - 8\sin x$
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trazar la recta. $y = -\\frac{2}{3}x + 1$
To draw the line \(y =-\frac{2}{3}x + 1\), plot the y - intercept \((0,1)\) and use the slope \(-\frac{2}{3}\) to find another point (e.g., \((3,-1)\) or \((-3,3)\)) and then draw…
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find the derivative of $g(x) = \\frac{1}{x^7}$.\ \ $g(x) = \\frac{1}{7x…
$g'(x)=-\frac{7}{x^8}$
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find the derivative of $f(x) = \\ln\\left(\\frac{x^6}{2x^5 - 7}\ ight)$…
$f'(x)=\frac{6}{x}-\frac{10x^4}{2x^5 - 7}$
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find the derivative of $f(x) = -15sin x + \frac{11}{x^4} + 3sqrt7{x} - …
A. $f'(x)= - 15\cos x-\frac{44}{x^{5}}+\frac{3}{7x^{\frac{6}{7}}}$
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question 8 find the derivative of $y = \\tan(3^{4x}+1)$. $\\frac{dy}{dx…
$\boldsymbol{\frac{dy}{dx} = 4\cdot 3^{4x}\ln3\cdot \sec^2(3^{4x}+1)}$ (the second option)
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find the derivative of $y = 12x^{4}+\frac{5}{x^{7}} - 8\\csc x$.\ \ $\\…
$y'=48x^3-\frac{35}{x^8}+8\csc x\cot x$ (the first option)
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write newton’s formula used to approximate a solution of the equation $…
D. $x_{n+1}=x_n - \frac{2x_n^3 - x_n - 15}{6x_n^2 - 1}; x_3 \approx 2.042527942$
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a sphere is to be designed with a radius of 72 in. use differentials to…
32,572.03 $\text{in}^3$
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determine if the function $f(x)=\\sqrt4{x^3}$ is differentiable at $x =…
$f(x)=\sqrt[4]{x^3}$ is not differentiable at $x = 0$ because $f'(0)$ is not defined.
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find the derivative of $f(x) = \\frac{2\\cos x}{9x^3 + 16}$.\ \ $\\bold…
$\boldsymbol{f'(x)=\frac{-18x^3\sin x -32\sin x -54x^2\cos x}{(9x^3+16)^2}}$ (the fourth option)
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what is $f(x) + f(x) + f(x)$? $3f(x)$ complete $3f(x) = 3x^2$ complete …
12
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find the average value of $f(x)=e^{2x}$ over the interval $0, ln 5$. a.…
d.) $\frac{12}{\ln5}$
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if f and g are the functions whose graphs are shown, let u(x) = f(x)g(x…
### Part (a): Find \( u'(1) \) #### Explanation: To find \( u'(1) \) where \( u(x) = f(x)g(x) \), we use the product rule: \( u'(x) = f'(x)g(x) + f(x)g'(x) \). We need to determin…
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write a function in any form that would match the graph shown below. an…
$f(x) = -\frac{125}{24}(x+6)(x+4)(x-8)$
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question write a function in any form that would match the graph shown …
$f(x)=-3(x+4)(x-5)^2$
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write a function in any form that would match the graph shown below.
$y=-\frac{5}{3}(x+3)^2(x-1)(x-2)$
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tinjiuh bseibhu answer attempt 1 out of 2 $f(x) = \\square$ submit answ…
$5x^2+5x-30$
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solve the integral \\(\\int e^{x}\\sqrt{5e^{x} + 4}\\ dx\\) with the fo…
a.) $\frac{2}{15}(5e^{x}+4)^{\frac{3}{2}}+c$
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$$int \tan^{9}xsec^{2}x dx$$ a.) $\frac{1}{10}\tan^{10}x + c$ b.) $\fra…
a.) $\frac{1}{10}\tan^{10}x + c$
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$$int 18x^3(3x^4 + 7)^9 dx$$ a.) $\frac{9}{5}(3x^4 + 7)^{10}+c$ b.) $\f…
d.) $\frac{3}{20}(3x^4 + 7)^{10}+c$
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$$int (12e^x - 7^x + 7x^5) dx$$ a.) $12e^x + \frac{7^x}{ln 7} + \frac{7…
b.) $12e^{x}-\frac{7^{x}}{\ln7}+\frac{7}{6}x^{6}+c$
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unit 5 — challenge 5.3: antiderivatives use the fundamental theorem of …
c.) $\int_{-2}^{1} 5x^4 dx = 33$
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use the order of operations to evaluate this expression. enter the numb…
17
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find the inverse of the function. \\( n(x) = sqrt3{x} - 2 \\) write you…
\( h^{-1}(x)=(x + 2)^3 \) (or in the form \( 1(x + 2)^3+0 \))
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find the inverse of the function. ( h(x) = sqrt{x - 3} ) write your ans…
The inverse function \( h^{-1}(x)=\boldsymbol{x^2 + 3} \) and the domain of the inverse function is \( x\geq\boldsymbol{0} \) (in the form \( x\geq\# \), here \(\# = 0\)).
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evaluate the following expression following the order of operations. $7…
28
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use the graph to determine a. the functions domain; b. the functions ra…
a. $[0,20]$ b. $[2,6]$ c. None d. $2$ e. $6$
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find the inverse of the function.\\ g(x) = \\sqrt{x} + 7\\ write your a…
\( g^{-1}(x)=(x - 7)^2 \), \( x\geq7 \)
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determine all intervals on which $f(x) \\leq 0$.
There are no intervals where $f(x) \leq 0$.
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question given $f(x) = -x^2 + x - 17$, find $f(-8)$
$-89$
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use the graph of f to find the value of f(0). f(0) = \\square
$4$
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the graph below is the function $f(x)$ determine which one of the follo…
\( f(a) \) is defined. (The rule that \( f(a) \) is defined is violated at \( x = 2 \) because there is an open circle at \( x = 2 \), meaning \( f(2) \) is not defined. The limit…
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find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriat…
\(\infty\)
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use the graph to determine (a) open intervals on which the function is …
(a) A. The function is increasing on the interval(s) $(2, \infty)$ (b) B. The function is never decreasing (c) The function is constant on the interval $(-\infty, 2)$
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question the function $f(x)$ is graphed below. how many points on the g…
1
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question the graph of ( y = f(x) ) is graphed below. what is the end be…
as $x \to \infty, y \to \infty$ and as $x \to -\infty, y \to \infty$
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select the correct answer from each drop - down menu. the graph of ( g(…
a horizontal asymptote at $y=3$ and an x-intercept at $x=-5$
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sketch a graph of: $f(x) = -2|x + 4| + 1$ before sketching the graph, d…
The graph is a downward-opening V with vertex (maximum point) at $(-4, 1)$, passing through $(-5, -1)$ and $(-3, -1)$.
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find f(g(x)) and g(f(x)) and determine whether the pair of functions f …
$f(g(x)) = 16x$ $g(f(x)) = 16x$ The functions $f$ and $g$ are **not inverses** of each other, since $f(g(x)) eq x$ and $g(f(x)) eq x$.
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use possible symmetry of the graph to determine whether it is the graph…
The function is neither even nor odd.
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the graph of $y = f(x)$ is shown below. according to the graph, what is…
1
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sketch the graph of the quadratic function $h(x) = 3x^2 - 12x + 9$ on t…
- Direction of opening: Upward. - Axis of symmetry: \( x = 2 \) (vertical line). - Vertex: \( (2,-3) \). - y - intercept: \( (0,9) \). - x - intercepts: \( (1,0) \), \( (3,0) \). …
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simplify. e^{\\ln x} = e^{\\ln 5} = e^{\\ln 3x}
$e^{\ln x} = x$ $e^{\ln 5} = 5$ $e^{\ln 3x} = 3x$
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the function g (graphed below in blue) is a transformation of function …
B. $f(x) - 4$
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select the correct answer. a ball is thrown up from a height of 400 fee…
C. \( t = 5 \)
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use the interactive graph below to sketch a graph of $y = 3^{4 - x} + 1…
1. Draw the horizontal asymptote $y=1$ (a dashed horizontal line through $y=1$) 2. Plot the points $(4, 2)$, $(3, 4)$, and $(5, \frac{4}{3})$ 3. Draw a curve that approaches $y=1$…
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solve the following system of equations graphically on the set of axes …
1. For $y=-x-2$: Plot points $(-2,0)$ and $(0,-2)$, then draw the line through them. 2. For $y=2x-8$: Plot points $(4,0)$ and $(0,-8)$, then draw the line through them. 3. The sol…
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score on last try: 0 of 1 pt. see details for more. at least one scored…
Positive derivative interval: \( (-2, 2) \) Negative derivative interval: \( (-\infty, -2) \cup (2, \infty) \)
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evaluate the piecewise function at the given values of the independent …
(a) $h(3)=5$ (b) $h(0)=2$ (c) $h(2)=3$
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sketch a graph of $f(x) = -\frac{1}{2}|x|$\ before sketching the graph,…
The graph is a downward-opening V with vertex at $(0, 0)$, passing through points $(2, -1)$ and $(-2, -1)$, with straight lines extending from the vertex through these points.
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given the functions $f(x) = 3x^4$ and $g(x) = 9 \\cdot 3^x$, which of t…
\( f(3) = g(3) \) (the option with \( f(3) = g(3) \))
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(int_{0}^{8} \frac{dx}{sqrt{1 + x}})
\( 4 \)
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kuta software - infinite calculus name_____________________________ ave…
2 ### Problem 2: \( v = -\frac{1}{x - 2} \); \([-3, -2]\)
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kuta software - infinite calculus average rates of change for each prob…
\( 2 \) ### Problem 2: \( v = -\frac{1}{x - 2} \); \([-3, -2]\)
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graph: $f(x) = -sqrt{x}$ step 1: evaluate the function to find three po…
The table is filled as above, and the graph is a curve passing through \((0,0)\), \((1,-1)\) and \((4,-2)\) with the domain \(x\geq0\) and decreasing for \(x\geq0\).
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what is the slope of this line? simplify your answer and write it as a …
$\frac{1}{6}$
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what is the slope of this line? simplify your answer and write it as a …
2
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what is the slope of this line? simplify your answer and write it as a …
1
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what is the slope of this line? simplify your answer and write it as a …
$1$
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what is the slope of this line? simplify your answer and write it as a …
2
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what is the slope of this line? simplify your answer and write it as a …
$\frac{3}{5}$
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graph $h(t) = 2(t - 2)^2 + 4$.
Plot the vertex $(2,4)$, symmetric points $(1,6)$, $(3,6)$, $(0,12)$, $(4,12)$, then draw an upward-opening parabola passing through these points.
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adding and subtracting using fractions a) $\frac{1}{6} + \frac{1}{6}$ b…
a) $\frac{1}{3}$ b) $\frac{2}{5}$ c) $\frac{3}{4}$ d) $\frac{3}{10}$ e) $\frac{19}{12}$ f) $\frac{35}{36}$ g) $\frac{1}{3}$ h) $\frac{7}{3}$ i) $\frac{25}{24}$ j) $1\frac{7}{10}$ …
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consider the graph of a function ( f ) shown below. use the graph to es…
a). Increasing: $(-\infty, -2) \cup (6, \infty)$ b). Decreasing: $(-2, 2) \cup (2, 6)$
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part a – numerical expressions (order of operations) write your own num…
One possible numerical expression is \(2^2\times(3 + 2)\) (which equals 20 using exponentiation, addition, and multiplication as three different operations). Another is \((9 - 4)^…
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part a – numerical expressions (order of operations) 1. evaluate the ex…
14
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given $f(x)=x + 1$ and $g(x)=x^{2}$, what is $(gcirc f)(x)$? $(gcirc f)…
$(g \circ f)(x) = (x + 1)^2$
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question 3 find the partition number(s) of ( r(x) = \frac{x^2(x^2 - 4)}…
A. x=-3, C. x=-2, F. x=0, H. x=2
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our base - 10 number system today is known as __ numerals. arabic greek…
A. Arabic ### Second Question (Muslim Mathematicians' Development)
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graph $f(t) = -3(t - 2)^2 + 1$. question help: video submit question
The graph is a downward-opening parabola with vertex at $(2, 1)$, passing through points $(1,-2)$, $(3,-2)$, $(0,-11)$, $(4,-11)$, and symmetric about the line $t=2$. Plot these p…
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15 multiple choice 1 point which geographic feature most helped medieva…
C. Fertile river valleys and navigable waterways