Test Mathematics also useful for physics

MATHS CLASS XI
LIMITS AND DERIVATIVES
PRACTICE PAPER 01

Time Allowed: 2 hrs Max. Marks: 50

SECTION – A (1 mark)

lim x n  3n
1. Find the positive integer n so that  108 .
x  3 x 3
lim x2  9
2. Evaluate: .
x3 x 3
lim sin x
3. Evaluate: .
x0 x (1  cos x)
lim sin x
4. Evaluate: .
x  x 
lim 1
5. Evaluate: x sin .
x0 x
 
6. If f(x) = x sinx, then find f '   .
2
2
7. Find the derivative of x cosx.

8. Find the derivative of 2x4 + x.

9. If f (x) = x100 + x99 + ... + x + 1, then f ′(1)

10. Find the derivative of (x2 +1)cos x.

SECTION – B (2 marks)

lim
11. Evaluate:
 sec x  tan x 

x
2
lim 2  x  2
12. Evaluate:
x0 x
2
mx  n, x  0
 lim
13. If f ( x )   nx  m, 0  x  1 , then for what integers m and n does both f ( x) and
 nx  m, x  1
3 x  0

lim
f ( x) exists.
x 1

14. Find the derivative of f (x) = ax + b, where a and b are non-zero constants, by first principle.

15. Find the derivative of f (x) = x3, by first principle.

16. Find the derivative of f (x) = sin x, by first principle.


Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 -