MATH 76 Activity 8/25 Flashcards

1

Evaluate \lim_{x\to∞}\frac{3x^3-14x^2+8x+6}{4x^3+2x^2-x-1}.

8
-7
-\frac{3}{4}
\frac{3}{4}

2

Evaluate \int_{\sqrt[3]{7}}^{\sqrt[3]{8}}14xe^{x^2}dx.

12e^6
\frac{1}{4}
\frac{24}{71}
7e

3

Evaluate \lim_{x\to2}\frac{x^2-3x+2}{x^2+x-6}.

1
3
\frac{1}{5}
\frac{1}{2}

4

Evaluate \int_3^8\frac{2x}{x^2-7}dx.

\ln\left(24\right)-\ln\left(8\right)
\ln\left(57\right)-\ln\left(2\right)
\ln\left(82\right)+\ln\left(7\right)
\ln\left(41\right)-\ln\left(6\right)

5

Evaluate\int_5^714xe^{x^2}dx.

14\left(e^{49}-e^{25}\right)
7\left(e^{49}-e^{25}\right)
7\left(e^{25}-e^{49}\right)
2\left(e^{49}-e^{25}\right)

6

Evaluate \int_{ }^{ }x\left(1+x^2\right)^{86}dx.

\frac{\left(1+x^2\right)^{87}}{174}+C
\frac{\left(1+x^2\right)^{87}}{174}
This integral cannot be evaluated.
\frac{\left(1+x^2\right)^{87}}{87}+C

7

Evaluate \lim_{x\to3}\left(x^2-9\right).

9
0
18
3

8

Evaluate \frac{d}{dx}\left(\cos\left(x^2+4\right)\right).

-2x\cos\left(x^2+4\right)
-2x\sin\left(x^2+4\right)
-x^2\sin\left(x^2+4\right)
2x\sin\left(x^2+4\right)

9

Evaluate \int_{ }^{ }4x^3\ dx.

x^4+C
12x^4+C
x^4
12x^2

10

Evaluate \int_{ }^{ }\cos\left(x\right)+\sin\left(x\right)dx.

-\sin\left(x\right)+\cos\left(x\right)+C
-\sin\left(x\right)-\cos\left(x\right)+C
\sin\left(x\right)-\cos\left(x\right)+C
\sin\left(x\right)+\cos\left(x\right)+C

11

Evaluate \frac{d}{dx}\left(\ln\left(\sin\left(x\right)\right)\right).

\cot\left(x\right)
\frac{\cos\left(x\right)}{\sin\left(x\right)}
\frac{\sin\left(x\right)}{x}
\frac{\cos\left(x\right)}{x}

12

Evaluate \int_{ }^{ }\frac{4}{x}dx.

-\frac{4}{x^2}+C
4+C
4\ln\left|x\right|+C
\ln\left(4\right)+C

13

Evaluate \frac{d}{dx}\left(e^{x^2}\right).

e^{x^2}
2xe^{x^2}
e^{2x}
2e^x

14

Evaluate \int_{ }^{ }\frac{x}{\sqrt{1-x^2}}dx.

-\frac{1}{\sqrt{1-x^2}}+C
\sqrt{1-x^2}+C
-\sqrt{1-x^2}+C
\frac{-\sqrt{1-x^2}}{2x}+C

15

Evaluate \frac{d}{dx}\left(3x-2\right)^3.

\left(3x-2\right)^2
3\left(3x-2\right)^2
27\left(3x-2\right)^2
9\left(3x-2\right)^2

16

Evaluate \frac{d}{dx}\left(\sqrt{2x+4}\right).

\frac{1}{\sqrt{2x+4}}
-\sqrt{2x+4}
\frac{1}{2\sqrt{2x+4}}
\frac{2}{\sqrt{2x+4}}

17

Evaluate \int_0^{\frac{\pi}{2}}24\cos\left(x\right)-8\sin\left(x\right)dx.

8
16
32
24

18

Evaluate \int_4^9\sqrt{x}dx.

65
\frac{42}{3}
\frac{38}{3}+C
\frac{38}{3}

19

Evaluate \frac{d}{dx}\left(4x^2\right).

8x
4x
8x^2
16x

20

Evaluate \int_{ }^{ }\sqrt{2x-8}\ dx.

\frac{1}{3}\sqrt{2x-8}^3+C
\frac{2}{3\sqrt{2x-8}}+C
\frac{1}{2}\sqrt{2x-8}^3+C
This integral cannot be evaluated.

MATH 76 Activity 8/25

Questions 20

MATH 76 Activity 8/25

Questions 20