Question 1

Find $\int_{0}^{4}(3 x+2) d x$ by using formulas from geometry.

Accepted Answer

The answer of Find $\int_{0}^{4}(3 x+2) d x$ by using...

Question 2

Find the slope of the tangent line to the graph of $f(x)=2 x^{2}+3 x$ at the point where $x=0$.

Accepted Answer

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

Question 3

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$, say so.
-$\lim _{x \rightarrow 2^{-}} f(x)$ where $f(x)= \begin{cases}x^{2}+x & \text { if } x<2 \ 3-5 x & \text { if } x \geq 2\end{cases}$

Accepted Answer

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

Question 4

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$, say so.
-$\lim _{x \rightarrow 7} \frac{x^{2}-3 x-28}{x-7}$

Accepted Answer

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

Question 5

$\lim _{x \rightarrow 2} \frac{|x-2|}{x-2}$

Accepted Answer

The answer of $\lim _{x \rightarrow 2} \frac{|x-2|}{x-2}$...

Question 6

Five 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 7

$\lim _{x \rightarrow \infty}(-1)$

Accepted Answer

The answer of $\lim _{x \rightarrow \infty}(-1)$...

Question 8

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$, say so.
-$\lim _{x \rightarrow 0} \frac{x^{3}+2 x-3}{x^{2}+5}$

Accepted Answer

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

Question 9

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$, say so.
-$\lim _{x \rightarrow-\infty} \frac{7 x-4}{x-4}$

Accepted Answer

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

Question 10

$\lim _{x \rightarrow 8^{-}} 12$

Accepted Answer

The answer of $\lim _{x \rightarrow 8^{-}} 12$...

Question 11

Find the slope of the tangent line to the graph of $f(x)=3 x^{2}-4$ at the point where $x=-2$.

Accepted Answer

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

Question 12

Find $\int_{0}^{5}(5-x) d x$ by using the formula for the area of a triangle.

Accepted Answer

The answer of Find $\int_{0}^{5}(5-x) d x$ by using the...

Question 13

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 14

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

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

Find the equation of the tangent line to the graph of $f(x)=-\frac{8}{x}$ at the point $(-2,4)$.

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

$\lim _{x \rightarrow 3^{-}} \sqrt{9-x_{2}}$

Accepted Answer

The answer of $\lim _{x \rightarrow 3^{-}} \sqrt{9-x_{2}}$...

Question 19

$\lim _{x \rightarrow 5^{-}} \sqrt{2 x-10}$

Accepted Answer

The answer of $\lim _{x \rightarrow 5^{-}} \sqrt{2 x-10}$...

Question 20

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$, say so.
-$\lim _{x \rightarrow 5} \frac{x^{2}-x-20}{x^{2}-25}$

Accepted Answer

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

Find $\int_{0}^{4}(3 x+2) d x$ by using formulas from geometry.

Find the slope of the tangent line to the graph of $f(x)=2 x^{2}+3 x$ at the point where $x=0$ .

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 2^{-}} f(x)$ where $f(x)= \begin{cases}x^{2}+x & \text { if } x<2 \\ 3-5 x & \text { if } x \geq 2\end{cases}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 7} \frac{x^{2}-3 x-28}{x-7}$

$\lim _{x \rightarrow 2} \frac{|x-2|}{x-2}$

Five 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?

$\lim _{x \rightarrow \infty}(-1)$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 0} \frac{x^{3}+2 x-3}{x^{2}+5}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow-\infty} \frac{7 x-4}{x-4}$

$\lim _{x \rightarrow 8^{-}} 12$

Find the slope of the tangent line to the graph of $f(x)=3 x^{2}-4$ at the point where $x=-2$ .

Find $\int_{0}^{5}(5-x) d x$ by using the formula for the area of a triangle.

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

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

Find the equation of the tangent line to the graph of $f(x)=-\frac{8}{x}$ at the point $(-2,4)$ .

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

$\lim _{x \rightarrow 3^{-}} \sqrt{9-x_{2}}$

$\lim _{x \rightarrow 5^{-}} \sqrt{2 x-10}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 5} \frac{x^{2}-x-20}{x^{2}-25}$

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 ∫04(3x+2)dx\int_{0}^{4}(3 x+2) d x∫04​(3x+2)dx by using formulas from geometry.

Find the slope of the tangent line to the graph of f(x)=2x2+3xf(x)=2 x^{2}+3 xf(x)=2x2+3x at the point where x=0x=0x=0 .

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→7x2−3x−28x−7\lim _{x \rightarrow 7} \frac{x^{2}-3 x-28}{x-7}limx→7​x−7x2−3x−28​

lim⁡x→2∣x−2∣x−2\lim _{x \rightarrow 2} \frac{|x-2|}{x-2}limx→2​x−2∣x−2∣​

Five 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→∞(−1)\lim _{x \rightarrow \infty}(-1)limx→∞​(−1)

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→0x3+2x−3x2+5\lim _{x \rightarrow 0} \frac{x^{3}+2 x-3}{x^{2}+5}limx→0​x2+5x3+2x−3​

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→−∞7x−4x−4\lim _{x \rightarrow-\infty} \frac{7 x-4}{x-4}limx→−∞​x−47x−4​

lim⁡x→8−12\lim _{x \rightarrow 8^{-}} 12limx→8−​12

Find the slope of the tangent line to the graph of f(x)=3x2−4f(x)=3 x^{2}-4f(x)=3x2−4 at the point where x=−2x=-2x=−2 .

Find ∫05(5−x)dx\int_{0}^{5}(5-x) d x∫05​(5−x)dx by using the formula for the area of a triangle.

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→2+f(x)\lim _{x \rightarrow 2^{+}} f(x)limx→2+​f(x)

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)

Find the equation of the tangent line to the graph of f(x)=−8xf(x)=-\frac{8}{x}f(x)=−x8​ at the point (−2,4)(-2,4)(−2,4) .

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

lim⁡x→3−9−x2\lim _{x \rightarrow 3^{-}} \sqrt{9-x_{2}}limx→3−​9−x2​​

lim⁡x→5−2x−10\lim _{x \rightarrow 5^{-}} \sqrt{2 x-10}limx→5−​2x−10​

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→5x2−x−20x2−25\lim _{x \rightarrow 5} \frac{x^{2}-x-20}{x^{2}-25}limx→5​x2−25x2−x−20​

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 $\int_{0}^{4}(3 x+2) d x$ by using formulas from geometry.

Find the slope of the tangent line to the graph of $f(x)=2 x^{2}+3 x$ at the point where $x=0$ .

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 7} \frac{x^{2}-3 x-28}{x-7}$

$\lim _{x \rightarrow 2} \frac{|x-2|}{x-2}$

Five 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?

$\lim _{x \rightarrow \infty}(-1)$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 0} \frac{x^{3}+2 x-3}{x^{2}+5}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow-\infty} \frac{7 x-4}{x-4}$

$\lim _{x \rightarrow 8^{-}} 12$

Find the slope of the tangent line to the graph of $f(x)=3 x^{2}-4$ at the point where $x=-2$ .

Find $\int_{0}^{5}(5-x) d x$ by using the formula for the area of a triangle.

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

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

Find the equation of the tangent line to the graph of $f(x)=-\frac{8}{x}$ at the point $(-2,4)$ .

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

$\lim _{x \rightarrow 3^{-}} \sqrt{9-x_{2}}$

$\lim _{x \rightarrow 5^{-}} \sqrt{2 x-10}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 5} \frac{x^{2}-x-20}{x^{2}-25}$