微積分
極限、導関数、最適化、関数挙動。
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question plot all intercepts and asymptotes of the following rational f…
Vertical Asymptote: $x=-2$ Horizontal Asymptote: $y=2$ x-intercept: $(-\frac{3}{2},0)$ y-intercept: $(0,\frac{3}{2})$ (Plot these features on the graph: vertical line at $x=-2$, h…
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evaluate $y = \\ln (x - 2)$ for the following values of $x$. round to t…
The Top Graph (the first graph from the top)
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score: 5/6 answered: 5/6 question 3 for $y = 8 \\sin 7x$, its amplitude…
Amplitude: \( 8 \), Period: \( \frac{2\pi}{7} \)
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evaluate $y = \\ln(x - 2)$ for the following values of $x$. round to th…
When \( x = 3 \), \( y = 0 \); when \( x = 4 \), \( y\approx0.693 \); when \( x = 6 \), \( y\approx1.386 \)
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let $y = \\sqrt{20} \\sin\\left(2\\pi x + 2e^2\ ight)$. what is the amp…
Amplitude: \( \sqrt{20} \) (or \( 2\sqrt{5} \)) Period: \( 1 \) Phase Shift: \( -\frac{e^2}{\pi} \)
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determine the amplitude and period of $-\\cos(5x)$ shown in this graph:…
amplitude = \( 1 \) period = \( \frac{2\pi}{5} \)
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which of the following is the graph of $y = e^x + 1$? three graphs are …
The Middle Graph (the second graph among the three)
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select the correct answer. which statement is true? a. inexhaustible re…
D. Exhaustible resources are scarce.
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select the correct answer. what does a production possibilities curve r…
D. a combination of two goods that can be produced using limited resources
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consider the following equation: f(x) = (x² + 4)/(4x² - 4x - 8) name th…
\( y=\frac{1}{4} \)
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c. read the story below and complete the gaps with transition words fro…
Although ## (2)
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consider the following equation: $f(x) = \\frac{x^2 + 4}{4x^2 - 4x - 8}…
Vertical asymptotes are at \(x=-1\) and \(x = 2\) because this is where the function is undefined.
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which equation is equivalent to \\(\\log_{3}(2x^{4} + 8x^{3}) - 3\\log_…
\( \log_3(2x + 8) = \log_3x^2 \) (the third option)
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consider the following equation: $f(x) = \\frac{x^2 + 4}{4x^2 - 4x - 8}…
The vertical asymptotes are \(x=-1\) and \(x = 2\)
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which is the graph of $y = \\frac{2}{x + 1} - 6$? (with a graph showing…
The graph of \(y = \frac{2}{x+1}-8\) has a vertical asymptote at \(x=-1\) and a horizontal asymptote at \(y = -8\).
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find the derivative of the following function. $f(z) = \\left(2z + e^{-…
$6(2z + e^{-z^2})^5(2 - 2ze^{-z^2})$
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find the derivative of the function. $y = -4e^{-3x^2}$ $\frac{dy}{dx} =…
$24x e^{-3x^2}$
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differentiate the following function. $f(x) = -5e^{2x}$ $\frac{d}{dx} \…
$-10e^{2x}$
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consider the function $g(x) = \\frac{10}{x}$. the vertical asymptote is…
- B. The domain of \(g(x)\) is the same as the domain of the parent function. - D. The range is the same as the range of the parent function. - F. The function \(g(x)\) decreases …
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find the derivative of the function below. $y = e^{10x}$ $\frac{dy}{dx}…
$10e^{10x}$
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consider the function $g(x) = \\frac{10}{x}$. the vertical asymptote is…
The vertical asymptote is \(x = 0\). The horizontal asymptote is \(y = 0\).
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the graph of the function has a vertical asymptote of x = 0 ✔ the graph…
all nonzero real numbers
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find the equation of the tangent line to the graph of the given functio…
$\frac{4}{5}x + \frac{9}{5}$
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the graph of the function has a vertical asymptote of x = \\boxed{\\qua…
The graph of the function has a vertical asymptote of \(x = 0\). The graph of the function has a horizontal asymptote of \(y = 0\).
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find the derivative of the function. k(x) = -9(6x² + 7)⁻⁶ k’(x) = \\squ…
$648x(6x^2 + 7)^{-7}$
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what is the domain of the function $y = \\log(x + 3)$? $\\bigcirc$ $(-\…
\((-3, \infty)\) (the last option, e.g., if options are labeled as D. \((-3, \infty)\), then D. \((-3, \infty)\))
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shilpas gym membership includes a one-time fee of $20. she then pays a …
The horizontal asymptote is \(y = 5\)
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shilpas gym membership includes a one-time fee of $20. she then pays a …
\(m = n\), so \(y=a_m/b_n\) is the horizontal asymptote.
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which explains how advances in online education will most likely affect…
A. Online education will likely reduce the cost of higher education, and provide greater access for different kinds of students.
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graph the following function on the axes provided. $f(x) = \\begin{case…
Graph a horizontal line segment from the point \((-6,1)\) (closed circle) to \((-3,1)\) (open circle) for the first part. Then graph the line \(y=x + 4\) from the point \((-3,1)\)…
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which consideration must a society address when deciding for whom to pr…
Who has the greatest need?
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section 5.2 - systems of linear equations in three variables and applic…
The system has one solution. The solution set is \(\{(4,-4,-5)\}\).
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question 3 (multiple choice worth 2 points) (04.03r mc) given $f(x) = \…
D. As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.
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question 5 (multiple choice worth 2 points) (04.03r mc) which equation …
x=12
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section 5.2 - systems of linear equations in three variables and applic…
The slopes are $-7$ and $3$.
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let r be the region enclosed by the graphs of $f(x) = \\ln(x^4 + 1)$ an…
\(22.536\)
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given $g(x)=x^2 - 5x$, find the equation of the secant line passing thr…
$y=-4x+12$
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evaluate the function graphically. find ( f(-3) )
\(-4\)
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evaluate the function graphically. find ( f(3) ) answer attempt 1 out o…
\(-5\)
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evaluate or simplify the expression without using a calculator. $e^{ln …
\( 3x^{3} \)
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find $f_{xx}(x,y)$, $f_{xy}(x,y)$, $f_{yx}(x,y)$, and $f_{yy}(x,y)$ for…
\( 12xy \)
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find $f_{xx}(x,y)$, $f_{xy}(x,y)$, $f_{yx}(x,y)$, and $f_{yy}(x,y)$ for…
\( 6y^{2}+60x^{2} \)
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graph all vertical and horizontal asymptotes of the rational function. …
Vertical asymptote: $x = 2$ Horizontal asymptote: $y = 0$ (To graph: Draw a vertical dashed line at $x=2$ and a horizontal dashed line at $y=0$ on the coordinate plane.)
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the logistic growth function $f(t) = \\frac{117,000}{1 + 5100e^{-t}}$ d…
117000
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below is the graph of $y = e^x$. transform it to make the graph of $y =…
Domain: \((-\infty, \infty)\) Range: \((-\infty, 0)\)
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evaluate the expression without using a calculator. \\(\\log_{2} \\frac…
\(-\frac{1}{2}\)
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use the graph of f(x) to find the limit. \\lim_{x \\to 8} f(x) = \\squa…
5
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use the graph of f(x) to find the limit.
\( 6 \)
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below is the graph of $y = e^x$. transform it to make the graph of $y =…
Domain: \((-\infty, \infty)\) Range: \((5, \infty)\)
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graph all vertical and horizontal asymptotes of the rational function. …
Vertical asymptote: $x = -2.5$; Horizontal asymptote: $y = 0$ (Graph: Draw a dashed vertical line at $x=-2.5$ and a dashed horizontal line at $y=0$ on the grid.)
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graph all vertical and horizontal asymptotes of the rational function. …
Vertical asymptote: $x=-3.5$ (dashed vertical line at $x=-3.5$); Horizontal asymptote: $y=0$ (x-axis, dashed or solid as required)
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graph all vertical and horizontal asymptotes of the rational function. …
Vertical asymptote: $x=4$; Horizontal asymptote: $y=0$ (Graph: Vertical line through (4,0), horizontal line along x-axis)
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find the domain of the function. $f(x)=\\sqrt{\\frac{6}{3+x}}$ write yo…
$(-3, \infty)$
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given $h(x)=x^3 + 2$, find the equation of the secant line passing thro…
$y=7x-4$
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given $f(x)=x^2 + x$, find the equation of the secant line passing thro…
$y=-3x + 12$
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try again your answer is incorrect. given $f(x)=x^3 - 2$, find the equa…
$y=12x-18$
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the point (-1, 0.5) lies on the graph of f⁻¹(x) = 2ˣ. based on this inf…
B. (0.5, -1) (assuming the options are labeled with letters, if not, the point (0.5, -1))
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of exponential functions h. t(x) = 5^x - 3 y = 0 y = -3 y = -5 done
\( y = - 3 \)
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identify the horizontal asymptote of each graph. t(x) = 6^x options: y …
\( y = 0 \)
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use what you know about translations of functions to analyze the graph …
First blank: decreasing; Second (8 units): up; Third (5 units): to the right (assuming the blanks are for "decreasing", "up", "to the right" respectively, based on function transf…
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exponential growth functions when initially observed, a jellyfish popul…
\( 240(1.14)^x \)
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question 3 1 pts which byod variation allows us to choose a device from…
CYOD
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use the graphs of f and g to evaluate the composite function. (f∘g)(-2)
4
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16. a) find the limit as ( x ) approaches 2 from the left, the limit as…
### Part (a) \( \lim_{x \to 2^-} f(x)=\boldsymbol{2} \), \( \lim_{x \to 2^+} f(x)=\boldsymbol{2} \), \( \lim_{x \to 2} f(x)=\boldsymbol{2} \) ### Part (b) \( \lim_{x \to 1^-} f(x)…
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express the sum using summation notation. use 1 as the lower limit of s…
$$\sum_{i=1}^{n} (3i - 1)$$
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question use technology to find 2 points and then graph the function ( …
\( y = - 5 \)
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find the indicated sum. \\(\\sum\\limits_{i=1}^{5}\\frac{(-1)^{i}}{(i +…
$-\frac{53}{144}$
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find the indicated sum. \\(\\sum\\limits_{i=1}^{4} i(i + 2)\\) \\(\\sum…
50
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state the domain and range of the function represented by the graph bel…
Domain of \(f\): \((-4,\infty)\), Range of \(f\): \((-\infty,\infty)\), The function is invertible (because it passes the horizontal line test, being strictly monotonic), Domain o…
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state the domain and range of the function represented by the graph bel…
Domain of the function: \( (-1, \infty) \) (all real numbers greater than - 1) Range of the function: \( (-\infty, \infty) \) (all real numbers) The function is invertible (passes…
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a dissentient opinion came from the aunt. \a most improper story to tel…
B. "You have undermined the effect of years of careful teaching."
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11. (6pts total) for the position function $x(t) = a\\cos(\\omega t)$ $…
Velocity \( v(2\pi) = \boldsymbol{0\space m/s} \), Acceleration \( a(2\pi) = \boldsymbol{-4\space m/s^{2}} \)
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let r be the shaded region bounded by $f(x) = 5e^{-\frac{x}{5}} + 3$, $…
\( 23.943 \)
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write an integral expression that will give the length of the path give…
\(\int_{3}^{9}\sqrt{1+3600x^{10}\sin^{2}(2x^{6})}dx\)
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let the region r be the area enclosed by the function $f(x) = e^x$ and …
\(10.711\)
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use vocabulary in writing explain how you could determine whether \\(\\…
Simplify $\frac{21}{120}$ to $\frac{7}{40}$, convert both to decimals ($0.175$ vs. $0.\overline{7}$), and compare—they do not have the same decimal equivalent.
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let the region r be the area enclosed the function $f(x) = x^{\\frac{1}…
For the integral in terms of \(x\): \(x_1 = 0\), \(x_2=8\), \(\int_{0}^{8}(2 - x^{\frac{1}{3}})dx\) For the integral in terms of \(y\): \(y_1 = 2\), \(y_2 = 4\), \(\int_{2}^{4}(y …
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exercises 4.10 antiderivatives score: 2/30 answered: 2/11 question 2 te…
\(\frac{2x^{9}}{9}+\frac{9x^{8}}{8}-\frac{5x^{4}}{4}-x\)
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consider the function $f(x) = 2x^8 + 4x^5 - 10x^2 - 5$. enter an antide…
\(\frac{2x^{9}}{9}+\frac{2x^{6}}{3}-\frac{10x^{3}}{3}-5x\)
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explaining situational irony both the aunt and the children were conver…
D. The aunt expects obedience from the children, but does not get it.
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a logistic growth model for world population, f(x), in billions, x year…
2107
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the logistic growth function $f(t) = \\frac{117,000}{1 + 5100e^{-t}}$ d…
1239
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the logistic growth function $f(t) = \\frac{117,000}{1 + 5100e^{-t}}$ d…
23
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the logistic growth function p(x)= \\frac{90}{1 + 271e^{-0.122x}} model…
44
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if 1100 square centimeters of material is available to make a box with …
\(3510.57\) cubic centimeters.
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score on last try: 0 of 4 pts. see details for more. next question get …
\(9534.13\) cubic centimeters.
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score on last try: 0 of 4 pts. see details for more. next question get …
\(9534.13\) cubic centimeters.
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question 8 find the point on the curve ( y = sqrt{x} ) that is closest …
\((3.50,1.87)\)
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question 27, 4.5.77 hw score: 25.93%, 7 of 27 points points: 0 of 1 sav…
# Explanation: ## Step1: Determine t for 2011 2011 - 2006 = 5, so \( t = 5 \). ## Step2: Calculate Population of Country B For Country B, \( A = 33.1e^{0.008t} \). Substitute \( t…
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find the point on the line y = -4x that is closest to the point (5, 0).…
\((0.29,-1.18)\)
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question 4 a microwaveable cup-of-soup package needs to be constructed …
Radius: \(3.12\) cm Height: \(11.45\) cm Minimum cost: \(10.1\) cents
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a rectangle is inscribed with its base on the x-axis and its upper corn…
Width \(=\frac{4\sqrt{6}}{3}\), Height \(=\frac{16}{3}\)
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if 1100 square centimeters of material is available to make a box with …
\(9535.94\)
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question 2 if 2300 square centimeters of material is available to make …
\(\frac{2300\sqrt{6900}}{9}\approx21253.9\) cubic centimeters.
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ancient egypt: pharaohs identify: use the word bank to identify each de…
1. Ramesses II 2. Tutankhamun 3. Howard Carter 4. Dynasty 5. Nefertiti 6. Akhenaten 7. Great House 8. Menes 9. Cleopatra VII 10. Hatshepsut
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a box with a square base and open top must have a volume of 48668 cm³. …
\(A(x)=x^{2}+\frac{194672}{x}\) \(A^{\prime}(x)=2x-\frac{194672}{x^{2}}\) \(x = 46\) \(A^{\prime\prime}(x)=2+\frac{389344}{x^{3}}\) \(6\)
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when you calculate (ln) 7, you would be finding the value of which of t…
$\log_e 7$
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if \\(\\ln x + \\ln(x - 6) = \\ln(5x)\\), then \\(x = \\) question help…
\(11\)
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a box with a square base and open top must have a volume of 48668 cm³. …
\(A(x)=x^{2}+\frac{194672}{x}\) \(A^{\prime}(x)=2x-\frac{194672}{x^{2}}\) \(A^{\prime}(x)=0\) when \(x = 46\) \(A^{\prime\prime}(x)=2+\frac{389344}{x^{3}}\) \(A^{\prime\prime}(46)…
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which function is represented by the graph below? options: $f(x) = -\\l…
A. \(f(x) = -\ln(2x)\)