Free Printable HC 5.2

1.

$\int_{ }^{ }\left(\frac{10}{x}\right)dx$

a)

10 ln |x| + C

b)

ln |10x | + C

c)

10 log | x | + C

d)

$10x^0\ +\ C$

2.

$\int_{ }^{ }\left(\frac{1}{2x+5}\right)dx$

a)

$\frac{1}{2}\ln\left|2x+5\right|+C$

b)

$\ln\left|2x+5\right|+C$

c)

$2\ln\left|2x+5\right|+C$

d)

$\frac{2}{5}\ln\left|2x+5\right|+C$

3.

$\int_2^5\left(\frac{1}{x-1}\right)\ dx$

a)

$\ln\left(5\right)-\ln\left(2\right)$

b)

$\ln\left(2\right)-\ln\left(5\right)$

c)

$\ln\left(4\right)$

d)

$-\ln\left(4\right)$

4.

$\int\csc\left(15x\right)\ dx$

a)

$-\frac{1}{15}\ln\left|\csc x+\cot x\right|+C$

b)

$-\frac{1}{15}\ln\left|\csc\left(15x\right)+\cot\left(15x\right)\right|+C$

c)

$15\ln\left|\csc\left(15x\right)+\cot\left(15x\right)\right|+C$

d)

$-\frac{1}{15}\ln\left|\cot\left(15x\right)\right|+C$

5.

TRUE or FALSE
If f is an invertible function and $f\left(a\right)=b$ , then $f^{-1}\left(b\right)=a.$

a)

TRUE

b)

FALSE

6.

The inverse has been reflected over which line?

a)

$y=x$

b)

$y=1$

c)

$y=0$

d)

$y=x+1$

7.

Match the graph of the function given below with the graph of its inverse function.

a)

b)

c)

d)

8.

Use the function $f\left(x\right)=x^3+x$ and the given real number $a=2$ to find $\left(f^{-1}\right)'\left(a\right).$

a)

$\frac{1}{13}$

b)

$\frac{1}{4}$

c)

$4$

d)

$13$

9.

Use the function $f\left(x\right)=x+4$ and the given real number $a=-1$ to find $\left(f^{-1}\right)'\left(a\right).$

a)

$-9$

b)

$1$

c)

$-11$

d)

$4$

10.

Use the function $f\left(x\right)=4x^2+5\ ;\ x\ge0$
and the given real number $a=21$
to find $\left(f^{-1}\right)'\left(a\right).$

a)

$\frac{1}{8}$

b)

$\frac{1}{2}$

c)

$\frac{1}{4}$

d)

$\frac{1}{16}$

HC 5.2 - 5.3 Quiz

Total questions: 10

Worksheet time: 50mins

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