Test: Limits And Derivatives (CBSE Level) - 2


25 Questions MCQ Test Mathematics For JEE | Test: Limits And Derivatives (CBSE Level) - 2


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QUESTION: 1

 is equal to 

Solution:

lt h->0 [sin(x+h)½ - sin(x)½]/h
Differentiate it with ‘h’
lt h->0 {cos(x+h)½ * ½(x+h)1/2] - 0}/1
lt h->0 {cos(x+h)½ * ½(x+h)1/2]
lt h->0 cos(x)½ / 2(x)½

QUESTION: 2

Solution:

Divide the numerator and denominator by x, so that given function becomes
f(x)=1+sinx/x/(1+cosx/x)
Now as x→∞.sinx/x→0 , because sin x would oscillate between +1 and -1, which in either case divided by ∞ would be 0. Thus the limit of the numerator would be 1. Like wise the limit of the denominator would also be 1.
Thus limit as a whole would be 1

QUESTION: 3

Solution:
QUESTION: 4

is equal to

Solution:

lim x→0 sin xn . (x)m . xn /(sin x)m.(x)m.xn
lim x→0 sin xn.(x)m.xn-m/xn.(sin x)m
Applying limits.
=0n-m = 0

QUESTION: 5

Solution:
QUESTION: 6

If G(x) =  then  has the value

Solution:
QUESTION: 7

then dy/dx is equal to

Solution:
QUESTION: 8

If f be a function such that f (9) = 9 and f ‘ (9) = 3, then   is equal to

Solution:
QUESTION: 9

  is equal to 

Solution:
QUESTION: 10

If f(x) = , x ∈ (0,1), then f'(x) is equal to 

Solution:
QUESTION: 11

If y = sin-11 x  and z = cos -1  then dy/dz = 

Solution:
QUESTION: 12

 is equal to 

Solution:
QUESTION: 13

The function, f(x) =  and f(a) = 0, is 

Solution:
QUESTION: 14

 is equal to 

Solution:
QUESTION: 15

 is equal to 

Solution:
QUESTION: 16

If sin x = then dx/dy is equal to 

Solution:
QUESTION: 17

 holds true for

Solution:
QUESTION: 18

Dervative  of tan  w.r.t  is

Solution:
QUESTION: 19

If y = log  then 

Solution:
QUESTION: 20

If y = log x , then yn = 

Solution:
QUESTION: 21

The derivative of sec-1  with respect to  at x = 1/x is 

Solution:
QUESTION: 22

 is equal to

Solution:
QUESTION: 23

 is eqaual to  

Solution:
QUESTION: 24

If y =  then dy/dx = 

Solution:
QUESTION: 25

then at x = 1, f(x) is

Solution: