Free Printable Basic Calculus

1.

Evaluate the following $\lim_{x\rightarrow3}\ \frac{3-x}{x^2-4x+3}$

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

2.

Evaluate the following $\lim_{y\rightarrow0}\ \frac{\sin7y}{y\left(7+y\right)}$

a)

7

b)

1

c)

$\frac{1}{7}$

3.

$\lim_{x\rightarrow1}\ \frac{\sqrt{x+3}-2}{x^2-1}$ Evaluate the following

a)

0

b)

$\frac{1}{4}$

c)

$\frac{1}{8}$

4.

The function f(x) is defined as following picture. Find the value of a and b such that f(x) is continuous at x=2

a)

$a=\frac{3}{2},\ b=\frac{3}{2}$

b)

$a=3,\ b=\frac{3}{4}$

c)

$a=\frac{3}{2},\ b=\frac{3}{4}$

5.

What is the derivative of y = 2π ?

a)

0

b)

2

c)

-2

d)

None of the above

6.

Find the derivative of

$\frac{d}{dx}\cos x$

a)

$\sin x$

b)

$-\sin x$

c)

$-\operatorname{cosec}x\cot x$

d)

$\sec2x$

7.

Find the derivative of

$\frac{d}{dx}\tan x$

a)

$\operatorname{cosec}x\cot x$

b)

$\sec x\ \tan x\$

c)

$\sec2x$

d)

$-\operatorname{cosec}x\cot x\$

8.

∫(4 - 18x)dx

a)

F(x) = -18

b)

F(x) = 4x - 9x²

c)

F(x) = 4x - 9x²+ C

d)

F(x) = (4 - 18x)² /2 + C

9.

Which of the following is the indefinite integral of $\frac{x^3}{2}+7$ ?

a)

$\frac{3x^2}{2}$

b)

$\frac{3x^2}{2}+7x+c$

c)

$\frac{x^4}{8}+7x+c$

d)

$\frac{x^4}{8}+c$

10.

Integrate $\sqrt{x}$ with respect to x

a)

$x^{\frac{1}{2}}+c$

b)

$\frac{1}{2}x^{-\frac{1}{2}}+\ c$

c)

$\frac{2}{3}x^{\frac{3}{2}}+\ c$

d)

$\frac{3}{2}x^{\frac{3}{2}}+\ c$

Basic Calculus

Total questions: 10

Worksheet time: 12mins

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