Question 1

Find the equation of the tangent line to the graph of $f(x)=-\frac{6}{x}$ at the point $(2,-3)$.

Accepted Answer

The answer of Find the equation of the tangent line...

Question 2

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$, say so.
-$\lim _{x \rightarrow 3} \frac{x^{2}-3 x}{x-3}$

Accepted Answer

The answer of find the value of the given limit...

Question 3

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$, say so.
-$\lim _{x \rightarrow 3^{-}} f(x)$

Accepted Answer

The answer of find the value of the given limit...

Question 4

During a two-week period the number of people in a town who have a virus follows the model $f(t)=15,000 e^{-.27 t}$, where $f(t)$ is the number of people who have the virus after $t$ days. Use a calculator to graph $y=f(t)$ for $0 \leq t \leq 14$, and determine $f^{\prime}(7)$. What does $f^{\prime}(7)$ tell about the situation?

Accepted Answer

@#IMG-DLM& 
@#LAT-DLM&
After 7 days, the

Question 5

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$, say so.
-$\lim _{x \rightarrow 0} \frac{\sin x}{4 x}$

Accepted Answer

The answer of find the value of the given limit...

Question 6

$\lim _{x \rightarrow 7^{-}} 11$

Accepted Answer

The answer of $\lim _{x \rightarrow 7^{-}} 11$...

Question 7

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$, say so.
-$\lim _{x \rightarrow 4^{+}} f(x)$ where $f(x)=\left\{\begin{array}{cc}2 x^{2}-7 & \text { if } x \leq 4 \ 4-3 x & \text { if } x>4\end{array}\right.$

Accepted Answer

The answer of find the value of the given limit...

Question 8

Find $\int_{2}^{6}(2 x-4) d x$ by using the formula for the area of a triangle.

Accepted Answer

The answer of Find $\int_{2}^{6}(2 x-4) d x$ by using...

Question 9

$\lim _{x \rightarrow-1^{+}}\left(4 x^{2}-5 x+1\right)$

Accepted Answer

The answer of $\lim _{x \rightarrow-1^{+}}\left(4 x^{2}-5 x+1\right)$...

Question 10

Four grams of a radioactive substance is placed in a vault. The function defined by $f(t)$ shown in the graph gives the amount remaining after $t$ years. At what (in grams per year) is the substance disintegrating after 12 years?

Accepted Answer

approximat

Question 11

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$, say so.
-$\lim _{x \rightarrow 4} \frac{x^{2}-8 x+16}{x^{2}-16}$

Accepted Answer

The answer of find the value of the given limit...

Question 12

Three grams of a radioactive substance is placed in a vault. The function defined by $f(t)$ shown in the graph gives the amount remaining after $t$ years. At what rate (in grams per year) is the substance disintegrating after 16 years?

Accepted Answer

approximat

Question 13

$\lim _{x \rightarrow 2}\left(x^{3}+x^{2}+x+1\right)$

Accepted Answer

The answer of $\lim _{x \rightarrow 2}\left(x^{3}+x^{2}+x+1\right)$...

Question 14

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$, say so.
-$\lim _{x \rightarrow \infty} \frac{5 x^{2}-1}{2 x^{2}+5 x+3}$

Accepted Answer

The answer of find the value of the given limit...

Question 15

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$, say so.
-$\lim _{x \rightarrow 4^{-}} f(x)$

Accepted Answer

The answer of find the value of the given limit...

Question 16

$\lim _{x \rightarrow 200} 3$

Accepted Answer

The answer of $\lim _{x \rightarrow 200} 3$...

Question 17

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$, say so.
-$\lim _{x \rightarrow 5} \sqrt{x^{2}-9}$

Accepted Answer

The answer of find the value of the given limit...

Question 18

$\lim _{x \rightarrow-2^{+}} \sqrt{2 x+4}$

Accepted Answer

The answer of $\lim _{x \rightarrow-2^{+}} \sqrt{2 x+4}$...

Question 19

Approximate the area under the graph of $f(x)=2 x^{2}-1$ from $x=1$ to $x=5$ and above the $x$-axis, using four rectangles. Let the height of each rectangle be the function value at the midpoint of the interval.

Accepted Answer

approximat

Question 20

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$, say so.
-$\lim _{x \rightarrow 0} \frac{\sin x}{3 x}$

Accepted Answer

The answer of find the value of the given limit...

Find the equation of the tangent line to the graph of $f(x)=-\frac{6}{x}$ at the point $(2,-3)$ .

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 3} \frac{x^{2}-3 x}{x-3}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 3^{-}} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow 3^{-}} f(x)$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 0} \frac{\sin x}{4 x}$

$\lim _{x \rightarrow 7^{-}} 11$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 4^{+}} f(x)$ where $f(x)=\left\{\begin{array}{cc}2 x^{2}-7 & \text { if } x \leq 4 \\ 4-3 x & \text { if } x>4\end{array}\right.$

Find $\int_{2}^{6}(2 x-4) d x$ by using the formula for the area of a triangle.

$\lim _{x \rightarrow-1^{+}}\left(4 x^{2}-5 x+1\right)$

Four grams of a radioactive substance is placed in a vault. The function defined by $f(t)$ shown in the graph gives the amount remaining after $t$ years. At what (in grams per year) is the substance disintegrating after 12 years?

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 4} \frac{x^{2}-8 x+16}{x^{2}-16}$

Three grams of a radioactive substance is placed in a vault. The function defined by $f(t)$ shown in the graph gives the amount remaining after $t$ years. At what rate (in grams per year) is the substance disintegrating after 16 years?

$\lim _{x \rightarrow 2}\left(x^{3}+x^{2}+x+1\right)$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow \infty} \frac{5 x^{2}-1}{2 x^{2}+5 x+3}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 4^{-}} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow 4^{-}} f(x)$

$\lim _{x \rightarrow 200} 3$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 5} \sqrt{x^{2}-9}$

$\lim _{x \rightarrow-2^{+}} \sqrt{2 x+4}$

Approximate the area under the graph of $f(x)=2 x^{2}-1$ from $x=1$ to $x=5$ and above the $x$ -axis, using four rectangles. Let the height of each rectangle be the function value at the midpoint of the interval.

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 0} \frac{\sin x}{3 x}$

Linear Functions, Equations, and Inequalities

Analysis of Graphs of Functions

Polynomial Functions

Rational, Power, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Analytic Geometry and Nonlinear Systems

The Unit Circle and Functions of Trigonometry

Trigonometric Identities and Equations

Applications of Trigonometry and Vectors

Further Topics in Algebra

Reference: Basic Algebraic Concepts

Filters

Exam 12: Limits, Derivatives, and Definite Integrals

Find the equation of the tangent line to the graph of f(x)=−6xf(x)=-\frac{6}{x}f(x)=−x6​ at the point (2,−3)(2,-3)(2,−3) .

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→3x2−3xx−3\lim _{x \rightarrow 3} \frac{x^{2}-3 x}{x-3}limx→3​x−3x2−3x​

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→3−f(x)\lim _{x \rightarrow 3^{-}} f(x)limx→3−​f(x)

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→0sin⁡x4x\lim _{x \rightarrow 0} \frac{\sin x}{4 x}limx→0​4xsinx​

lim⁡x→7−11\lim _{x \rightarrow 7^{-}} 11limx→7−​11

Find ∫26(2x−4)dx\int_{2}^{6}(2 x-4) d x∫26​(2x−4)dx by using the formula for the area of a triangle.

lim⁡x→−1+(4x2−5x+1)\lim _{x \rightarrow-1^{+}}\left(4 x^{2}-5 x+1\right)limx→−1+​(4x2−5x+1)

Four grams of a radioactive substance is placed in a vault. The function defined by f(t)f(t)f(t) shown in the graph gives the amount remaining after ttt years. At what (in grams per year) is the substance disintegrating after 12 years?

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→4x2−8x+16x2−16\lim _{x \rightarrow 4} \frac{x^{2}-8 x+16}{x^{2}-16}limx→4​x2−16x2−8x+16​

Three grams of a radioactive substance is placed in a vault. The function defined by f(t)f(t)f(t) shown in the graph gives the amount remaining after ttt years. At what rate (in grams per year) is the substance disintegrating after 16 years?

lim⁡x→2(x3+x2+x+1)\lim _{x \rightarrow 2}\left(x^{3}+x^{2}+x+1\right)limx→2​(x3+x2+x+1)

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→∞5x2−12x2+5x+3\lim _{x \rightarrow \infty} \frac{5 x^{2}-1}{2 x^{2}+5 x+3}limx→∞​2x2+5x+35x2−1​

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→4−f(x)\lim _{x \rightarrow 4^{-}} f(x)limx→4−​f(x)

lim⁡x→2003\lim _{x \rightarrow 200} 3limx→200​3

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→5x2−9\lim _{x \rightarrow 5} \sqrt{x^{2}-9}limx→5​x2−9​

lim⁡x→−2+2x+4\lim _{x \rightarrow-2^{+}} \sqrt{2 x+4}limx→−2+​2x+4​

Approximate the area under the graph of f(x)=2x2−1f(x)=2 x^{2}-1f(x)=2x2−1 from x=1x=1x=1 to x=5x=5x=5 and above the xxx -axis, using four rectangles. Let the height of each rectangle be the function value at the midpoint of the interval.

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→0sin⁡x3x\lim _{x \rightarrow 0} \frac{\sin x}{3 x}limx→0​3xsinx​

Linear Functions, Equations, and Inequalities

Analysis of Graphs of Functions

Polynomial Functions

Rational, Power, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Analytic Geometry and Nonlinear Systems

The Unit Circle and Functions of Trigonometry

Trigonometric Identities and Equations

Applications of Trigonometry and Vectors

Further Topics in Algebra

Reference: Basic Algebraic Concepts

Filters

Find the equation of the tangent line to the graph of $f(x)=-\frac{6}{x}$ at the point $(2,-3)$ .

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 3} \frac{x^{2}-3 x}{x-3}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 3^{-}} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow 3^{-}} f(x)$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 0} \frac{\sin x}{4 x}$

$\lim _{x \rightarrow 7^{-}} 11$

Find $\int_{2}^{6}(2 x-4) d x$ by using the formula for the area of a triangle.

$\lim _{x \rightarrow-1^{+}}\left(4 x^{2}-5 x+1\right)$

Four grams of a radioactive substance is placed in a vault. The function defined by $f(t)$ shown in the graph gives the amount remaining after $t$ years. At what (in grams per year) is the substance disintegrating after 12 years?

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 4} \frac{x^{2}-8 x+16}{x^{2}-16}$

Three grams of a radioactive substance is placed in a vault. The function defined by $f(t)$ shown in the graph gives the amount remaining after $t$ years. At what rate (in grams per year) is the substance disintegrating after 16 years?

$\lim _{x \rightarrow 2}\left(x^{3}+x^{2}+x+1\right)$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow \infty} \frac{5 x^{2}-1}{2 x^{2}+5 x+3}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 4^{-}} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow 4^{-}} f(x)$

$\lim _{x \rightarrow 200} 3$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 5} \sqrt{x^{2}-9}$

$\lim _{x \rightarrow-2^{+}} \sqrt{2 x+4}$

Approximate the area under the graph of $f(x)=2 x^{2}-1$ from $x=1$ to $x=5$ and above the $x$ -axis, using four rectangles. Let the height of each rectangle be the function value at the midpoint of the interval.

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 0} \frac{\sin x}{3 x}$