Home
Class 12
MATHS
If f(x) = {{:((1)/(e^(1//x))",",x ne 0),...

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

A

`underset(x rarr 0^(-))(lim) f(x) = 0`

B

`underset(x rarr 0^(+))(lim) f(x) = 1`

C

f(x) is discontinuous at x = 0

D

f(x) is continuous at x = 0

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Similar Questions

Explore conceptually related problems

f(x)= {((1)/(e^(4x) + 1)",",x ne 0),(0",",x = 0):} Examine the continuity of f(x) at x= 0

f(x) = {((|x|)/(x)",","if" x ne 0),(0",","if" x= 0):}

A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0):} , then f(x) is(a) continuous at x = 0 ,(b) continuous at x = 1 (c)differentiable at x = 0

If f(x) = {{:((sin^(-1)x)^(2)cos((1)/(x))",",x ne 0),(0",",x = 0):} then f(x) is

f(x)= {((1- cos 4x)/(8x^(2))",",x ne 0),(k",",x= 0):} . If the function f(x) is continuous at x= 0, then find k.

Let f(x)={{:(x sin.(1)/(x)",",x ne0),(0",",x=0):}} and g(x)={{:(x^(2)sin.(1)/(x)",", x ne 0),(0",", x=0):}} Discuss the graph for f(x) and g(x), and evaluate the continuity and differentiabilityof f(x) and g(x).

Show that, f(x)= {((e^((1)/(x))-1)/(e^((1)/(x))+1)",",x ne 0),(0",",x=0):} . Is discontinuous at x= 0

Show the function, f(x) = {{:((e^(1//x)-1)/(e^(1//x)+1)",","when",x ne 0),(0",","when",x = 0):} has non-removable discontinuity at x = 0

f(x)= {((|sin x|)/(x)",",x ne 0),(1",",x=0):} Examine the continuity of f(x), x= 0

Examine the continuity of the function f(x) = {(|x|.cos ((1)/(x))",","if" x ne 0),(0",","if" x = 0):} at x= 0