What is the correct partial fraction form for $\frac{1}{(x-1)(x+2)}$?

$\frac{A}{x-1} + \frac{B}{x+2}$

$\frac{A}{x-1} + \frac{Bx+C}{x+2}$

$\frac{A}{(x-1)^2} + \frac{B}{x+2}$

MTH165 Unit 2: Differential and Integral Calculus - MCQ Practice | B. Tech. CSE

1 $What is the derivative of the product of two functions, and ?$

A.

B.

C.

D.

2 $What is the derivative of with respect to ?$

A.

B.

C.

D.

3 $If, find .$

A.

B.

C.

D.

4 $If and, what is ?$

A.

B.

C.

D.

5 $Find the derivative of the implicit function .$

A.

B.

C.

D.

6 $Logarithmic differentiation is most useful for functions of the form:$

A.

B.

C.

D.

7 $If, what is ?$

A.

B.

C.

D.

8 $Which of the following is a property of the indefinite integral?$

A.

None of these

B.

C.

D.

9 $What is the formula for integration by parts?$

A.

B.

C.

D.

10 $In the integration by parts method using the ILATE rule, what does 'L' stand for?$

A.

Logarithmic

B.

Linear

C.

Long

D.

Limit

11 $What is the correct partial fraction form for ?$

A.

B.

C.

D.

12 $Evaluate if is an odd function.$

A.

B.

C.

D.

13 $What is the derivative of ?$

A.

B.

C.

D.

14 $Find .$

A.

B.

C.

D.

15 $If and, find .$

A.

B.

C.

D.

16 $Differentiate .$

A.

B.

C.

D.

17 $If, find .$

A.

B.

C.

D.

18 $Evaluate for .$

A.

B.

C.

D.

19 $Evaluate .$

A.

B.

C.

D.

20 $Calculate .$

A.

B.

C.

D.

21 $To integrate, the standard result is:$

A.

B.

C.

D.

22 $Which trigonometric substitution is suitable for ?$

A.

B.

C.

D.

23 $Which property allows splitting into ?$

A.

Additivity of limits

B.

Change of variable

C.

Linearity property

D.

Integration by parts

24 $Evaluate .$

A.

B.

C.

D.

25 $Find .$

A.

B.

C.

D.

26 $What is the derivative of ?$

A.

B.

C.

D.

27 $If, what is ?$

A.

B.

C.

D.

28 $Find if and .$

A.

B.

C.

D.

29 $What is the form of partial fraction for ?$

A.

B.

C.

D.

None of these

30 $Evaluate .$

A.

B.

C.

D.

31 $If, find the value of .$

A.

B.

C.

D.

32 $Find the derivative of .$

A.

B.

C.

D.

33 $Determine the partial fraction decomposition form for .$

A.

B.

C.

D.

34 $Calculate .$

A.

B.

C.

D.

35 $What is ?$

A.

B.

C.

D.

36 $If, differentiate to find at the point where derivatives exist.$

A.

B.

C.

D.

37 $Evaluate .$

A.

B.

C.

D.

38 $Which rule is applied to differentiate ?$

A.

Quotient Rule

B.

Power Rule

C.

Product Rule

D.

Chain Rule

39 $Evaluate .$

A.

B.

C.

D.

40 $If, then is:$

A.

B.

C.

D.

41 $Find .$

A.

B.

C.

D.

42 $In integration by parts for, the best choice for is:$

A.

B.

C.

D.

43 $If, what is the first step in finding the derivative?$

A.

Use the product rule immediately

B.

Use the power rule

C.

Take the natural logarithm of both sides

D.

Integrate both sides

44 $Evaluate .$

A.

B.

C.

D.

45 $What is the derivative of a constant function ?$

A.

B.

C.

D.

46 $What is the partial fraction form for ?$

A.

B.

C.

D.

47 $Which of the following represents the Chain Rule?$

A.

B.

C.

D.

48 $Calculate .$

A.

B.

C.

D.

49 $If is an even function, what is ?$

A.

B.

C.

D.

50 $Find for .$

A.

B.

C.

D.

Unit 2: Differential and Integral Calculus - Practice Quiz

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