Home
Class 12
MATHS
Let f(x) = {{:((cos x-e^(x^(2)//2))/(x^(...

Let `f(x) = {{:((cos x-e^(x^(2)//2))/(x^(3))",",x ne 0),(0",",x = 0):}`, then
Statement I f(x) is continuous at x = 0.
Statement II `lim_(x to 0 )(cos x-e^(x^(2)//2))/(x^(3)) = - (1)/(12)`

A

Statement I is correct, Statement II is also correct, Statement II is the correct explanation of Statement I

B

Statement I is correct, Statement II is also correct, Statement II is not the correct explanation of Statement I

C

Statement I is correct, Statement II is incorrect

D

Statement I is incorrect, Statement II is correct.

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise EXERCISE 4|3 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

If f(x) = {{:(x((e^(1//x) - e^(-1//x))/(e^(1//x)+e^(-1//x)))",",x ne 0),(" "0",",x = 0):} , then at x = 0 f(x) is

Let f(x) = {:{((3x+4tanx)/x, x ne0),(k, x = 0):} then f is continuous at x = 0 for

Let f(x)={(xsin(1/x), x ne 0),(k, x=0):} find k if f is continuous at x=0,

Let f(x) = {:{((sinx)/x + cosx, when x ne 0),(2, when x = 0):} show that f (x) is continouous at x = 0.

If function defined by f(x) = {{:((sin 3x)/(2x)"," ,x != 0),(k + 1",", x = 0):} is continuous at x = 0 , then value of k is

Find k in R if f(x) = {:{((cos^2 x - sin^2 x -1)/(sqrt(x^2+1) - 1), x ne 0), (k, x = 0):} is continuous at 0.

Prove that the function f(x) = {{:(x cos 1/x"," , "when " x != 0),(0",", "when " x = 0):} is continuous at x = 0

Let f(x) = {:{((1-cosax)/(xsinx), x ne 0),(1/2, if x = 0):} If f is continuous at x=0, find a.

Evaluate : lim_(x rarr 0) (e^(3x)-e^(2x))/x .