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Test: Limits And Derivatives - 2 - JEE MCQ


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25 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Limits And Derivatives - 2

Test: Limits And Derivatives - 2 for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Limits And Derivatives - 2 questions and answers have been prepared according to the JEE exam syllabus.The Test: Limits And Derivatives - 2 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Limits And Derivatives - 2 below.
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Test: Limits And Derivatives - 2 - Question 1

 is equal to 

Detailed Solution for Test: Limits And Derivatives - 2 - Question 1

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

Test: Limits And Derivatives - 2 - Question 2

Detailed Solution for Test: Limits And Derivatives - 2 - Question 2

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

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Test: Limits And Derivatives - 2 - Question 3

Test: Limits And Derivatives - 2 - Question 4

is equal to

Detailed Solution for Test: Limits And Derivatives - 2 - Question 4

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

Test: Limits And Derivatives - 2 - Question 5

Test: Limits And Derivatives - 2 - Question 6

If G(x) =  then  has the value

Test: Limits And Derivatives - 2 - Question 7

then dy/dx is equal to

Test: Limits And Derivatives - 2 - Question 8

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

Test: Limits And Derivatives - 2 - Question 9

  is equal to 

Test: Limits And Derivatives - 2 - Question 10

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

Test: Limits And Derivatives - 2 - Question 11

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

Test: Limits And Derivatives - 2 - Question 12

 is equal to 

Test: Limits And Derivatives - 2 - Question 13

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

Test: Limits And Derivatives - 2 - Question 14

 is equal to 

Test: Limits And Derivatives - 2 - Question 15

 is equal to 

Test: Limits And Derivatives - 2 - Question 16

If sin x = then dx/dy is equal to 

Test: Limits And Derivatives - 2 - Question 17

 holds true for

Test: Limits And Derivatives - 2 - Question 18

Dervative  of tan  w.r.t  is

Test: Limits And Derivatives - 2 - Question 19

If y = log  then 

Test: Limits And Derivatives - 2 - Question 20

If y = log x , then yn = 

Test: Limits And Derivatives - 2 - Question 21

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

Test: Limits And Derivatives - 2 - Question 22

 is equal to

Test: Limits And Derivatives - 2 - Question 23

 is eqaual to  

Test: Limits And Derivatives - 2 - Question 24

If y =  then dy/dx = 

Test: Limits And Derivatives - 2 - Question 25

then at x = 1, f(x) is

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