CALCULUS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Solution

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PROBLEM 41 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SOLUTION

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PROBLEM 57

Find the derivative

 

(UME 2008, Question 36, set U03, type A)

 

SOLUTION

 

Answer Option C

 

PROBLEM 58

Differentiate  

(a) xcosx (b) xsinx  (c) – xcosx (d) –xsinx (UME 2008, Question 37, Set U03, type A)

Solution

 

Answer Option B

 

PROBLEM 59

Find the minimum value of the function

y = x (1+x) 

(UME 2008, Question 38 set U03, type A)

 

SOLUTION

 

PROBLEM 60

Evaluate

(UME 2008, Question 39 set U03, type A)

 

Answer Option D

 

PROBLEM 61

 Evaluate  (a)  0 (b) 1  (c) 2 (d) 3

(UME 2008, Question 40 set U03, type A)

 

 Solution 

  Answer: Option C

 

 PROBLEM 62

 If y = 3cos 4x,  equals (a) 6sin8x (b) –24sin4x  (c) 12sin4x (d) –12sin4x  

 (UME 2009, Question 36, Set U03)

 

Solution

Answer: Option D

 

Question 63

If s = (2 + 3t)(5t – 4), find  when t =  secs

(a) 0 units per sec (b) 15 units per sec. (c) 22 units per sec (d) 26 units per sec. (UME 2009, Question 37, Set U03)

Solution

 

 

PROBLEM 64

What value of x will make the function x(4– x) maximum

(a)  4 (b) 3 (c) 2 (d)  1

(UME 2009, Question 36, Set U03)

Solution

 

Answer: Option C

 

Problem 65

The distance traveled by a particle from a fixed point is given as s = (t³ – t² – t +5)cm. Find the minimum distance that the particle can cover from the fixed point. 

(a) 2.3cm (b) 4.0cm  (c) 5.2 cm (d) 6.0 cm (UME 2009, Question 39, Set U03)

 

Solution

 

The minimum distance will be when t = 1sec

S = 1³ – 1² – 1 + 5 = 4 cm (Answer Option B)

 

Question 66

Evaluate  (UME 2009, Question 40, Set U03)

Answer: tanθ +k