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Joljol P.

Calculus 1 / AB

2 hours ago

joljolpo960@gmail.com

AB

Andres B.

Calculus 1 / AB

8 hours ago

how many positive integers not exceeding 200 and divisible by 2 or 3

NM

Nobin M.

Calculus 1 / AB

10 hours ago

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SA

Shakir A.

Calculus 1 / AB

1 day, 14 hours ago

123

JC

Jessica C.

Calculus 1 / AB

2 days, 3 hours ago

a. It can be shown that the inequalities $$ 1-\frac{x^{2}}{6}<\frac{x \sin x}{2-2 \cos x}<1 $$ hold for all values of $x$ close to zero (except for $x=0$ ). What, if anything, does this tell you about $$ \lim _{x \rightarrow 0} \frac{x \sin x}{2-2 \cos x} ? $$ Give reasons for your answer. b. Graph $y=1-\left(x^{2} / 6\right), \quad y=(x \sin x) /(2-2 \cos x),$ and $y=1$ together for $-2 \leq x \leq 2 .$ Comment on the behavior of the graphs as $x \rightarrow 0$

LM

Lisa M.

Calculus 1 / AB

2 days, 3 hours ago

Use the graphs of $f$ and $g$ in the accompanying figure to find the limits that exist. If the limit does not exist, explain why. $$ \begin{array}{ll}{\text { (a) } \lim _{x \rightarrow 2}[f(x)+g(x)]} & {\text { (b) } \lim _{x \rightarrow 0}[f(x)+g(x)]} \\ {\text { (c) } \lim _{x \rightarrow 0^{+}}[f(x)+g(x)]} & {\text { (d) } \lim _{x \rightarrow 0^{-}}[f(x)+g(x)]} \\ {\text { (e) } \lim _{x \rightarrow 0^{+}} \frac{f(x)}{1+g(x)}} & {\text { (f) } \lim _{x \rightarrow 2} \frac{1+g(x)}{f(x)}} \\ {\text { (g) } \lim _{x \rightarrow 0^{+}} \sqrt{f(x)}} & {\text { (h) } \lim _{x \rightarrow 0^{-}} \sqrt{f(x)}}\end{array} $$

NC

Nate C.

Calculus 1 / AB

2 days, 3 hours ago

Water pours into the tank here at the rate of 4 $\mathrm{ft}^{3} / \mathrm{min}$ . The tank's cross-sections are $4-\mathrm{ft}$ -diameter semicircles. One end of the tank is movable, but moving it to increase the volume compresses a spring. The spring constant is $k=100 \mathrm{lb} / \mathrm{ft}$ . If the end of the tank moves 5 $\mathrm{ft}$ against the spring, the water will drain out of the tank hole in the bottom at the rate of $5 \mathrm{ft}^{3} / \mathrm{min} .$ Will the movable end reach the hole before the tank overflows? Graph cannot copy

PL

Patrick L.

Calculus 1 / AB

2 days, 3 hours ago

For $f(x)=\frac{P(x)}{Q(x)}$ to have an asymptote at $y=2$ then the polynomials $P(x)$ and $Q(x)$ must have what relation?

PB

Pedro B.

Calculus 1 / AB

2 days, 3 hours ago

For the following exercises, find the horizontal and vertical asymptotes. $$ f(x)=\frac{1}{x-1}-2 x $$

JM

Jacob M.

Calculus 1 / AB

2 days, 3 hours ago

Find the point on the graph of $f(x)=x^{3}$ such that the tangent line at that point has an $x$ intercept of $6 .$

SN

Sabrina N.

Calculus 1 / AB

2 days, 3 hours ago

A small town in Ohio commissioned an actuarial firm to conduct a study that modeled the rate of change of the townÔÇÖs population. The study found that the townÔÇÖs population (measured in thousands of people) can be modeled by the function $P(t)=-\frac{1}{3} t^{3}+64 t+3000,$ where $t$ is measured in years. a. Find the rate of change function P?(t) of the population function. b. Find P?(1), P?(2), P?(3), and P?(4). Interpret what the results mean for the town. c. Find P??(1), P??(2), P??(3), and P??(4). Interpret what the results mean for the townÔÇÖs population.

AT

Alex T.

Calculus 1 / AB

2 days, 3 hours ago

In the following exercises, use direct substitution to show that each limit leads to the indeterminate form 0$/ 0$ . Then, evaluate the limit. $$\lim _{x \rightarrow 2} \frac{x-2}{x^{2}-2 x}$$

VM

Vanessa M.

Calculus 1 / AB

2 days, 3 hours ago

The base is the region enclosed by $y=x^{2}$ and $y=3 .$ The cross sections perpendicular to the $y$-axis are squares.

CW

Chelsea W.

Calculus 1 / AB

2 days, 3 hours ago

For the function $f$ whose graph is given, determine the following limits. $$ { a. }\lim _{x \rightarrow 2} f(x) \quad \text { b. } \lim _{x \rightarrow-3^{+}} f(x) $$ $$ { c. }\lim _{x \rightarrow-3^{-}} f(x) \quad \text { d. } \lim _{x \rightarrow-3} f(x) $$ $$ { e. }\lim _{x \rightarrow 0^{+}} f(x) \quad \text { f. } \lim _{x \rightarrow 0^{-}} f(x) $$ $$ { g. }\lim _{x \rightarrow 0} f(x) \quad \text { h. } \lim _{x \rightarrow \infty} f(x) $$ $$ { i. }\lim _{x \rightarrow-\infty} f(x) $$

VS

Victoria S.

Calculus 1 / AB

2 days, 3 hours ago

Consider the point $(x, y)$ lying on the graph of the line $2 x+4 y=5 .$ Let $L$ be the distance from the point $(x, y)$ to the origin $(0,0) .$ Write $L$ as a function of $x .$

KT

Kathy T.

Calculus 1 / AB

2 days, 3 hours ago

In Exercises $27-30,$ find the (a) slope and (b) $y$ -intercept, and (c) graph the line. $$\frac{x}{3}+\frac{y}{4}=1$$

PF

Patrick F.

Calculus 1 / AB

2 days, 3 hours ago

Finding a Region In Exercises $11 - 14 ,$ the integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral. $$\int _ { - 2 } ^ { 1 } \left[ ( 2 - y ) - y ^ { 2 } \right] d y$$

PP

Patrick P.

Calculus 1 / AB

2 days, 3 hours ago

Estimating a Limit Numerically In Exercises $5-10$ , complete the table and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. $$\lim _{x \rightarrow 0} \frac{\sqrt{x+1}-1}{x}$$

AF

After F.

Calculus 1 / AB

2 days, 3 hours ago

Secant and Tangent Lines Discuss the relationship between secant lines through a fixed point and a corresponding tangent line at that fixed point.

NC

Nate C.

Calculus 1 / AB

2 days, 3 hours ago

Gene regulation Genes produce molecules called mRNA that go on to produce proteins. High concentrations of protein inhibit the production of mRNA, leading to stable gene regulation. This process has been modeled (see Section 10.3 ) to show that the concentration of mRNA overtime is given by the equation $m(t)=\frac{1}{2} e^{-t}(\sin t-\cos t)+\frac{1}{2}$ What is the rate of change of mRNA concentration as a function of time?

JH

James H.

Calculus 1 / AB

2 days, 3 hours ago

The upper right-hand corner of a piece of paper, $ 12 $ in. by $ 8 $ in., as in the figure, is folded over to the bottom edge. How would you fold it so as to minimize the length of the fold? In other words, how would you choose $ x $ to minimize $ y $?

at

Alex T.

Calculus 1 / AB

2 days, 3 hours ago

A retailer has been selling 1200 tablet computers a week at $ \$ 350 $ each. The marketing department estimates that an additional 80 tablets will sell each week for every $ \$ 10 $ that the price is lowered. (a) Find the demand function. (b) What should the price be set at in order to maximize revenue? (c) If the retailer's weekly cost function is $$ C(x) = 35,000 + 120x $$ what price should it choose in order to maximize its profit?

EH

Edward H.

Calculus 1 / AB

2 days, 3 hours ago

The velocity of a car was read from its speedometer at 10-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car.

PS

Penny S.

Calculus 1 / AB

2 days, 3 hours ago

The velocity function (in meters per second) is given for a particle moving along a line. Find (a) the displacement and (b) the distance traveled by the particle during the given time interval. $ v(t) = t^2 - 2t - 3 $, $ 2 \le t \le 4 $

JC

James C.

Calculus 1 / AB

2 days, 3 hours ago

Sketch the area represented by $ g(x) $. Then find $ g'(x) $ in two ways: (a) by using Part 1 of the Fundamental Theorem and (b) by evaluating the integral using Part 2 and then differentiating. $ \displaystyle g(x) = \int^x_1 t^2\,dt $

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