Free Printable Revision PSPM

1.

Does the limit of the f(x) exists?

\lim_{x\rightarrow0}f\left(x\right)

?

a)

$0$

b)

$1$

c)

$-1$

d)

DOES NOT EXIST.

2.

Does the limit of the f(x) exists?

\lim_{x\rightarrow4}f\left(x\right)

?

a)

$3$

b)

$-3$

c)

$0$

d)

limit DOES NOT EXIST.

3.

Use the given function to determine the value of the limit

a)

DNE

b)

-12

c)

10

d)

0

4.

If $\lim_{x\rightarrow c}f\left(x\right)=3$ , $\lim_{x\rightarrow c}g\left(x\right)=-2$ , $\lim_{x\rightarrow c}h\left(x\right)=4$ then find $\lim_{x\rightarrow c}\left[f\left(x\right)\cdot5g\left(x\right)\right]$

a)

-30

b)

-40

c)

60

d)

-80

5.

If $\lim_{x\rightarrow c}f\left(x\right)=3$ , $\lim_{x\rightarrow c}g\left(x\right)=-2$ , $\lim_{x\rightarrow c}h\left(x\right)=4$ then find $\lim_{x\rightarrow c}\left[7-g\left(x\right)\right]^2$

a)

81

b)

25

c)

9

d)

45

6.

If $\lim_{x\rightarrow c}f\left(x\right)=3$ , $\lim_{x\rightarrow c}g\left(x\right)=-2$ , $\lim_{x\rightarrow c}h\left(x\right)=4$ then find $\lim_{x\rightarrow c}\left(\frac{2f\left(x\right)+3h\left(x\right)}{h\left(x\right)-g\left(x\right)}\right)$

a)

3

b)

2

c)

1

d)

0

7.

$\lim_{x\rightarrow11}\ \ \frac{x^2-121}{x-11}\ =\ ....$

a)

22

b)

21

c)

20

d)

19

e)

18

8.

$\lim_{x\rightarrow-3}\ \ \frac{x+3}{x^2-9}\ =\ ....$

a)

0

b)

$-6$

c)

6

d)

$-\frac{1}{6}$

e)

$\frac{1}{6}$

9.

$\lim_{x\rightarrow2}\ \ \frac{x^3-8}{x-2}\ =\ ....$

a)

0

b)

$\infty$

c)

12

d)

$-12$

e)

$\frac{1}{12}$

10.

$\lim_{x\rightarrow3}\ \ \frac{x^2+2x-15}{x^2-x-6}\ =\ ....$

a)

$\frac{5}{8}$

b)

$\frac{8}{5}$

c)

$-\frac{8}{5}$

d)

$-\frac{5}{8}$

e)

0

11.

a)

-1/4

b)

-1/2

c)

1

d)

2

12.

a)

4

b)

8

c)

12

d)

16

e)

18

13.

a)

-30

b)

-27

c)

15

d)

30

e)

36

14.

Jika $f\left(x\right)=\frac{1-x}{2-\sqrt{x^2+3}},$ maka nilai dari $\lim_{x\rightarrow1}\ f\left(x\right)$ adalah ....

a)

$0$

b)

$\frac{1}{2}$

c)

$1$

d)

$2$

e)

$4$

15.

Find the derivative of

a)

sinx

b)

-sinx

c)

-cscx cotx

d)

sec²x

16.

$\frac{\text{d}}{\text{d}x}\left(2\sin x+x^3\right)$

a)

$2\cos x+3x^2$

b)

$-2\cos x+3x^2$

c)

$2\cos x+4x^4$

d)

$2\cos x+2x^2$

e)

$-2\cos x+2x^2$

17.

Find dy/dx if y = cos⁵x

a)

5cos⁴x

b)

-5sin⁴x

c)

5cos⁴xsinx

d)

-5cos⁴xsinx

18.

What is the derivative of $y=2\sin^34x$

a)

$6\sin^24x\cos4x$

b)

$24\sin^24x$

c)

$24\sin^24x\cos4x$

d)

$6\sin^24x$

19.

What is the derivative of $y=\tan\ \left(5x+1\right)-\cos\ 2x$

a)

$5\sec^2\left(5x+1\right)+2\sin2x$

b)

$5\sec^2\left(5x+1\right)-2\sin2x$

c)

$\sec^2\left(5x+1\right)+\sin2x$

d)

$\sec^2\left(5x+1\right)-\sin2x$

20.

What is the derivative of

y=\ln2x

a)

$\frac{dy}{dx}=\frac{1}{2x}$

b)

$\frac{dy}{dx}=\frac{1}{x}$

c)

$\frac{dy}{dx}=\frac{2}{x}$

d)

$\frac{dy}{dx}=\frac{1}{x^2}$

21.

What is the derivative of

y=2\ln\left(x^2+3x\right)

a)

$\frac{dy}{dx}=\frac{2x}{x^2+3x}$

b)

$\frac{dy}{dx}=\frac{2}{x^2+3x}$

c)

$\frac{dy}{dx}=\frac{2x+3}{x^2+3x}$

d)

$\frac{dy}{dx}=\frac{4x+6}{x^2+3x}$

22.

What is the derivative of

y=\ln\left(\frac{x}{2x+1}\right)

a)

$\frac{dy}{dx}=\frac{1}{x}-\frac{2}{2x+1}$

b)

$\frac{dy}{dx}=\frac{1}{x}-\frac{1}{2x+1}$

c)

$\frac{dy}{dx}=\frac{1}{x}+\frac{2}{2x+1}$

d)

$\frac{dy}{dx}=\frac{1}{x}+\frac{1}{2x+1}$

23.

What is the derivative of

y=\ln\left(xe^x\right)

a)

$\frac{dy}{dx}=\frac{1}{x}+e^x$

b)

$\frac{dy}{dx}=\frac{1}{x}+1$

c)

$\frac{dy}{dx}=\frac{1}{xe^x}$

d)

$\frac{dy}{dx}=\frac{1}{x}-1$

24.

What is the derivative of

y=\ln\left(x^2+3\right)^5

a)

$\frac{dy}{dx}=\frac{10x}{x^2+3}$

b)

$\frac{dy}{dx}=\frac{5x}{x^2+3}$

c)

$\frac{dy}{dx}=\frac{2x}{x^2+3}$

d)

$\frac{dy}{dx}=\frac{10}{x^2+3}$

25.

What is the derivative of

y=\ln\left(\frac{x^2+3}{x^3}\right)

a)

$\frac{dy}{dx}=\frac{x}{x^2+3}-\frac{3}{x}$

b)

$\frac{dy}{dx}=\frac{2x}{x^2+3}-\frac{3}{x}$

c)

$\frac{dy}{dx}=\frac{1}{x^2+3}-\frac{1}{x^3}$

d)

$\frac{dy}{dx}=\frac{x}{x^2+3}-\frac{1}{x^3}$

26.

What is the derivative of

y=e^{2x+3}

a)

$\frac{dy}{dx}=e^{2x+3}$

b)

$\frac{dy}{dx}=2e^{2x+3}$

c)

$\frac{dy}{dx}=2xe^{2x+3}$

d)

$\frac{dy}{dx}=3e^{2x+3}$

27.

What is the derivative of

y=2e^{\sqrt{x+3}}

a)

$\frac{dy}{dx}=\frac{e^{\sqrt{x+3}}}{\sqrt{x+3}}$

b)

$\frac{dy}{dx}=\frac{2e^{\sqrt{x+3}}}{\sqrt{x+3}}$

c)

$\frac{dy}{dx}=2e^{\sqrt{x+3}}$

d)

$\frac{dy}{dx}=e^{\sqrt{x+3}}$

28.

What is the derivative of

y=5e^{4x-x^2}

a)

$\frac{dy}{dx}=5e^{4x-x^2}$

b)

$\frac{dy}{dx}=5\left(2-x\right)e^{4x-x^2}$

c)

$\frac{dy}{dx}=10\left(2-x\right)e^{4x-x^2}$

d)

$\frac{dy}{dx}=\left(4-2x\right)e^{4x-x^2}$

29.

What is the derivative of

y=e^{3x}+\frac{1}{2e^{2x}}

a)

$\frac{dy}{dx}=3e^{3x}-\frac{1}{2e^{2x}}$

b)

$\frac{dy}{dx}=3e^{3x}-\frac{1}{e^{2x}}$

c)

$\frac{dy}{dx}=e^{3x}-\frac{1}{e^{2x}}$

d)

$\frac{dy}{dx}=e^{3x}-\frac{1}{2e^{2x}}$

30.

What is the derivative of

y=xe^x

a)

$\frac{dy}{dx}=e^x+xe^x$

b)

$\frac{dy}{dx}=e^x-xe^x$

c)

$\frac{dy}{dx}=xe^x$

d)

$\frac{dy}{dx}=e^x$

31.

What is the derivative of

y=\frac{e^x}{x}

a)

$\frac{dy}{dx}=\frac{xe^x+e^x}{x}$

b)

$\frac{dy}{dx}=\frac{e^x-xe^x}{x^2}$

c)

$\frac{dy}{dx}=\frac{xe^x-e^x}{x^2}$

d)

$\frac{dy}{dx}=\frac{xe^x-e^x}{x}$

32.

Find the derivative of f(x) = 6x³⁰-2x¹⁵ + 4x³ - 2x + 1

a)

f'(x) = 18x²⁹+ 30x¹⁵ + 12x³

b)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x²

c)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² - 2

d)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² +1

33.

Use the product rule to find the derivative. $f\left(x\right)\ =\ -x^3\left(3x^4-2\right)$

a)

$-3x^2+12x^3$

b)

$-21x^3+6x$

c)

$-21x^6+6x^2$

d)

$-84x^6-6x^2$

34.

Let f(x) = (x - 1)(x + 2). Find f'(0)

a)

0

b)

1

c)

2

d)

3

35.

a)

-20x⁶ + 10x

b)

-70x⁶ + 30x⁴ + 10x

c)

5x² + 10x - 3

d)

-10x⁷ - 94x⁵ + 5x² - 3

36.

a)

f '(x) =-8x⁵ + 12x³ + 8x/3x⁸ + 6x⁴ + 3

b)

f '(x) = 48x⁵ - 36x³

c)

f '(x) =-24x⁵ + 36x³ + 24x/16x⁴ - 24x² + 9

d)

f '(x) =-12x³ + 8x/9x⁸ + 18x⁴ + 9

37.

a)

f '(x) =3x³ + 12/4x⁵

b)

f '(x) = 36x⁶

c)

f '(x) =16x³ - 9x²/9x⁶ + 18x³ + 9

d)

f '(x) =4x⁶ + 16x³/3x⁶ + 6x³ + 3

Revision PSPM

Total questions: 37

Worksheet time: 3hrs 5mins

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