微積分
極限、導數、最優化與函數性質。
-
refer to the figure below which contains the graph of ( f(x) ), the der…
\(4.25\)
-
refer to the figure below which contains the graph of f(x), the derivat…
\(4.4\)
-
the figure to the right gives the number of farms in millions from 1920…
1950
-
use the graph below to fill in each entry of the grid with positive, ne…
| | \( f \) | \( f' \) | \( f'' \) | |---|---|---|---| | \( A \) | negative | positive | positive | | \( B \) | zero | zero | positive | | \( C \) | positive | negative | negative…
-
use the graph below to fill in each entry of the grid with positive, ne…
| | \(f\) | \(f^{\prime}\) | \(f^{\prime\prime}\) | |---|---|---|---| | \(A\) | negative | zero | positive | | \(B\) | positive | positive | negative | | \(C\) | positive | zero |…
-
for each function, determine the long run behavior \\( \\frac { x ^ { 3…
\(\frac{x^{3}+1}{x^{2}+2}\) has No horizontal asymptote. \(\frac{x^{2}+1}{x^{3}+2}\) has a Horizontal asymptote at \(y = 0\). \(\frac{x^{2}+1}{x^{2}+2}\) has a Horizontal asymptot…
-
the graph of the following function has one relative extreme point. fin…
The relative extreme point is \((-\frac{1}{2},-6)\). Is the relative extreme point a relative maximum or a relative minimum? Relative maximum.
-
differentiate. y = - \\frac{70}{x^{6}} \\frac{d}{dx} \\left( - \\frac{7…
\(\frac{420}{x^{7}}\)
-
let ( y = 4x^{2}+4x + 4 ). if ( delta x=0.3 ) at ( x = 4 ), use linear …
\(10.8\)
-
use linear approximation to estimate the amount of paint in cubic centi…
\(3200000\pi\approx 10053096.49\) cubic centimeters
-
let ( y = 5sqrt{x} ). find the change in ( y, delta y ) when ( x = 4 ) …
\(\Delta y = 0.24695\), \(dy=0.25\)
-
let ( y = 4x^{2} ). find the change in ( y ), ( delta y ) when ( x = 1 …
\(\Delta y = 0.84\) \(dy=0.8\)
-
let ( y=\tan (4 x + 7) ). find the differential ( d y ) when ( x = 5 ) …
When \(dx = 0.4\), \(dy\approx2.02\); when \(dx=0.8\), \(dy\approx4.03\)
-
let ( y=\tan (2 x+7) ). find the differential ( d y ) when ( x=2 ) and …
When \(dx = 0.2\), \(dy = 0.4\); when \(dx=0.4\), \(dy = 0.8\)
-
let ( y = \tan(2x + 7) ). find the differential ( dy ) when ( x = 2 ) a…
When \(dx = 0.2\), \(dy = 0.8\); when \(dx=0.4\), \(dy = 1.6\)
-
the circumference of a sphere was measured to be 70 cm with a possible …
The maximum error in the calculated surface area is approximately \(22.3\) \(cm^{2}\). The relative error in the calculated surface area is approximately \(0.0143\).
-
in the figure, the straight line is tangent to the graph of ( f(x) ). f…
\( f(5)=7 \) \( f^{\prime}(5)=\frac{6}{5} \)
-
the circumference of a sphere was measured to be 89 cm with a possible …
The relative error is approximately \(0.0112\)
-
suppose that ( f(800)=3000 ) and ( f^{prime}(800)=10 ). estimate each o…
(a) \(3010\) (b) \(3005\) (c) \(2990\) (d) \(2980\) (e) \(2997.5\)
-
the circumference of a sphere was measured to be 89 cm with a possible …
The maximum error in the calculated surface area is approximately \(28.33\) \(cm^{2}\). The relative error in the calculated surface area is approximately \(0.0112\).
-
given the function below f(x)=sqrt3{-50 x^{3}+175} find the equation of…
\(0.03203\)
-
given the function below f(x)=sqrt3{-50 x^{3}+175} find the equation of…
\( L(x)=-2x + 7 \) \( L(1.1)=4.8 \) \( |\text{error}|\approx0.03203 \)
-
the linear approximation at ( x = 0 ) to ( sin(7x) ) is ( a + bx ) wher…
\(A = 0\) and \(B=7\)
-
use linear approximation, i.e. the tangent line, to approximate \\frac{…
\(0.996\)
-
use linear approximation, i.e. the tangent line, to approximate $\\sqrt…
\(L(x)=\frac{1}{14}x+\frac{7}{2}\); the approximation for \(\sqrt{49.2}\) is \(7.014285714\)
-
answer the following true or false: if ( y = 8x^{2} ) and you know the …
False
-
a circle is inside a square. the radius of the circle is decreasing at …
\(30 + 36\pi\) square meters per hour.
-
a circle is inside a square. the radius of the circle is decreasing at …
\(30 + 36\pi\approx30+36\times3.14=30 + 113.04=143.04\)
-
question 7 extra credit an inverted pyramid is being filled with water …
\(\frac{875}{36}\text{ cm/sec}\)
-
at the end of the holiday season in january, the sales at a department …
The sales are falling at a rate of \(-0.018\) thousand dollars per day on January 9.
-
at noon, ship a is 40 miles due west of ship b. ship a is sailing west …
\(23.72\)
-
gravel is being dumped from a conveyor belt at a rate of 40 cubic feet …
\(\frac{32}{125\pi}\approx0.0815\)
-
at the end of the holiday season in january, the sales at a department …
\(2.090\)
-
the altitude (height) of a triangle is increasing at a rate of 1.5 cm/m…
\(-\frac{5}{3}\)
-
the volume of a sphere of radius ( r ) is ( v=\frac{4}{3} pi r^{3} ). a…
\(48.4\pi\approx152.05\) \(\frac{cm^{3}}{min}\)
-
there are 8 problems in this section, but you only need to complete 5. …
\(6\pi\)
-
differentiate ( f(t)=8^{-9 t+2} ). ( f^{prime}(t)= )
\(-9\ln 8\cdot8^{-9t + 2}\)
-
the population of toledo, ohio, in the year 2000 was approximately 510,…
\(P'(6)\approx30075\) people per year
-
what does f(21)=30 imply? a. when the price per computer is $3000, for …
A. When the price per computer is \(\$2100\), for every \(\$100\) price increase, the sales decrease by \(8000\) computers.
-
the population of toledo, ohio, in the year 2000 was approximately 510,…
a. \(P(t)=510000(1.046)^t\) b. \(P^{\prime}(t)=510000(1.046)^t\ln(1.046)\) c. \(P^{\prime}(6)\approx29835\)
-
suppose that 5 mg of a drug is injected into the bloodstream. let f(t) …
\(2.925\)
-
let ( f(x)=x^{4x} ). use logarithmic differentiation to determine the d…
\(f^{\prime}(x)=x^{4x}(4\ln x + 4)\) \(f^{\prime}(1)=4\)
-
suppose that 5 mg of a drug is injected into the bloodstream. let f(t) …
- For “What is the meaning of \( f(2) = 3 \)?”: A. 2 hours after the drug was injected, the amount present in the bloodstream is 3mg. - For “What is the meaning of \( f^{\prime}(2…
-
let $f(x)=\\ln x^{6}(x + 2)^{5}(x^{2}+7)^{5}$ hint: use the properties …
\(\frac{6}{x}+\frac{5}{x + 2}+\frac{10x}{x^{2}+7}\)
-
homework assignment 6.7 exponential and logarithmic mode due friday by …
(a) \(P(t)=9200e^{0.07t}\) (b) \(16106\)
-
let ( f(t) ) be the temperature of a cup of coffee ( t ) minutes after …
- For \(f(9) = 130\): D. 9 minutes after the coffee has been poured, the temperature of the cup of coffee is 130 degrees. - For \(f^{\prime}(9)=-7\): C. 9 minutes after the coffee…
-
let ( f(t) ) be the temperature of a cup of coffee ( t ) minutes after …
D. 9 minutes after the coffee has been poured, the temperature of the cup of coffee is 130 degrees.
-
a marketing specialist determines that when a certain product is releas…
\( f'(t)=\frac{5}{t\ln(5)} \) \( f'(3)\approx1.039 \) For the interpretation of \( f(3) = 903 \): Since \( f(t) \) models the number of social - media references to the product an…
-
homework assignment 6.7 exponential and logarithmic mod due friday by 1…
The initial population at \(t = 0\) is \(5000\). The size of the bacterial population after 3 hours is \(2560000\).
-
suppose that ( f(900)=4000 ) and ( f^{prime}(900)=20 ). estimate each o…
\(4020\)
-
homework assignment 6.7 exponential and logarithmic model due friday by…
The size of the bacterial population after 40 minutes is approximately \(3780\). The size of the bacterial population after 4 hours is \(384000\).
-
an analysis of the daily output of a factory assembly line shows that a…
73
-
homework assignment 6.7 exponential and logarithmic models due friday b…
Half - life: \(50\) minutes. Formula: \(G(t)=348\times2^{-\frac{t}{50}}\). Amount after \(80\) minutes: \(131.54\) grams.
-
you go to the doctor and he gives you 13 milligrams of radioactive dye.…
\(39\)
-
suppose that ( f(x)=3 x^{2} ). (a) what is the average rate of change o…
\(6x\)
-
evaluate the expression. \\( \\arccos \\left( \\cos \\frac { 2 \\pi } {…
C. \(\frac{2\pi}{3}\)
-
find the area of the region in the first quadrant bounded by the line (…
\(\frac{5}{2}+5\ln5\)
-
find the exact value by using a half - angle identity. tan(75°) a. - 2 …
B. \(2+\sqrt{3}\)
-
use an identity to write the expression as a single trigonometric funct…
\(D.\ \cos4x\)
-
use a sum or difference identity to find the exact value. \\( \\frac { …
A. \(\sqrt{3}\)
-
use a sum or difference identity to find the exact value. tan(-15°) a. …
C. $\sqrt{3}-2$
-
use identities to write each expression as a function of $\\theta$. $\\…
A. $-\sin\theta$
-
use identities to find the exact value. $\\cos \\frac { 7 \\pi } { 12 }…
B. \(\frac{\sqrt{3}}{2}\)
-
make a sketch to show a case in which the area bounded by two curves is…
A.
-
write the expression in terms of sine and cosine, and simplify so that …
A. \(1+\cot x\)
-
complete the sentence so the result is an identity. let x be any real n…
A. \(\cot^{2}x\)
-
complete the sentence so the result is an identity. let x be any real n…
C. 1
-
use a geometric formula to find the area between the graphs of ( y = f(…
150
-
calculate $\\int_{2}^{7}3x dx$, given the following. $\\int_{2}^{7}x dx…
\(67.5\)
-
score: 33.33%, 4 of 12 points points: 0 of 1 calculate \\( \\int_{2}^{9…
\(721\)
-
which of the rectangles below are both left and right rectangles? selec…
E. Rectangle D
-
evaluate the integral. int_{1}^{3} x e^{-x^{2}} d x int_{1}^{3} x e^{-x…
\(0.184\)
-
evaluate the integral. $$ \\int_{2}^{3}\\left(3 x^{3}+2\ ight) d x $$ $…
\(\frac{203}{4}\)
-
evaluate the integral. int_{1}^{5}(2 x+8) d x int_{1}^{5}(2 x+8) d x=sq…
\(56\)
-
evaluate the integral int_{5}^{8} 8 , dx int_{5}^{8} 8 , dx = (simplify…
\(24\)
-
answer the following questions about ( f(x)=4x + 140 ). (a) calculate t…
\( 20 \)
-
use geometric formulas to find the unsigned area between the graph of y…
\(32\pi\)
-
use geometric formulas to find the unsigned area between the graph of (…
\(\frac{341}{2}\)
-
the main, or central, idea of the passage is individuals with eidetic m…
It highlights the limitations of eidetic memory.
-
edwards v. south carolina is significant because it limited states abil…
restrict the freedom of assembly.
-
though the outcomes of schenck and new york times differed, what did th…
The government can limit speech that causes harm.
-
a circle is growing, its radius increasing by 2 mm per second. find the…
\(201.062\)
-
given ( y = 2x^{2}+5x ), find ( \frac{dy}{dt} ) when ( x=-5 ) and ( \fr…
\(-30\)
-
suppose that x and y are related by the given equation and use implicit…
\(\frac{-4x^{3}y - y^{4}}{x^{4}+4xy^{3}}\)
-
cities should provide free access to gyms and fitness centers for teena…
The first option (the one that starts with "Promoting healthy habits among teenagers...") best distinguishes the claim.
-
for ( y = f(x) = 6x^{3}, x = 5 ), and ( delta x = 0.02 ) find a) ( delt…
a) \(\Delta y\approx9.0360\) b) \(dy = 18x^{2}dx\) c) \(dy = 9.00\)
-
solve the equation for solutions over the interval $0,2\\pi)$. write so…
A. The solution set is \(\{0.7080,0.8628\}\)
-
solve the equation for exact solutions over the interval $0,2\\pi)$. $9…
B. The solution is the empty set.
-
use the fundamental theorem of calculus to evaluate the following defin…
$12\ln 2$
-
read the excerpt. what does madisons analogy, liberty is to faction wha…
Liberty is crucial but can fuel divisions, like air fuels fire.
-
45. which statement best represents the current freedom of speech prote…
Schools can't limit general expressions of political views but can limit obscenity.
-
use the given function f to answer parts (a) through (f). f(x)=e^{x + 3…
\(f^{-1}(x)=\ln(x - 1)-3\)
-
18. daves writing teacher gave him constructive criticism on his last s…
Limit the amount of details so he doesn’t bog down the story.
-
multiple choice 1 point 11 derek has a credit card with a $1000 credit …
\(\$200\)
-
10 multiple choice 1 point how can your credit score impact your financ…
Your credit score can determine whether you are approved for a loan and what the interest rate on that loan will be ### Question 11
-
find the value or values of c that satisfy the equation $\\frac{f(b)-f(…
\(-\frac{3}{2}\)
-
review activity: synthesizing diverse perspectives a new look at the la…
- First question: The influence student debt and having a college degree have on graduates. - Second question: Student debt and college degrees both have an impact on career and l…
-
question find the y - intercept and equation of the horizontal asymptot…
- \(y\) - intercept: \((0,-11)\) - Horizontal Asymptote: \(y=-7\)
-
determine all critical points for the following function. f(x)=2x(8 - x…
\(f^\prime(x)=8(8 - x)^{2}(2 - x)\)
-
you are presenting in front of your class about the effect of acts of k…
Acts of kindness can improve individual well - being and strengthen communities. In this presentation, I will explore both the benefits and potential limitations of small acts of …