If {:(f(x),=(20^x + 3^x - 6^x- 10^x)/(1-...

If `{:(f(x),=(20^x + 3^x - 6^x- 10^x)/(1-cos 8x),",","for"x != 0),(,=(k/16)log(10/3)cdotlog 2, ",","for"x = 0):}` is continuous at x = 0, then the value of k is

A

(a) `sin^(2) 30^(@)`

B

(b) `3^(log3(1/2))`

C

(c) `root(3)(1/4)`

D

(d) `(log_(2)2)/(2)`

Verified by Experts

The correct Answer is:

B

Similar Questions

Explore conceptually related problems

{:(f(x),=(1-cos 3x)/(x tan x),",","for" x != 0),(,=k, ",","for" x = 0):} If f(x) is continuous at x = 0, the value of k is

{:(f(x),=(10^x + 7^x - 14^x- 5^x)/(1-cos x),",","for"x != 0),(,=10/7, ",","for"x = 0):} , then f(x) is

If {:(f(x),=log_(1-3x)(1+3x),",",x != 0),(,=k, ",",x = 0):} is continuous at x = 0, then the value of k is

If {:(f(x),=(log)(sec^2x)^(cot^2x),",","for"x != 0),(,=k, ",","for"x = 0):} is continuous at x = 0 then k is

If f(x) = {((sin 2x)/(5x), ",", "when" x != 0),(k, ",", "when" x = 0):} is continuous at x = 0, then the value of k will be

If f(x) = {((log_(e )x)/(x-1), ",", x != 1),(k, ",", x = 1):} is continuous at x = 1, then the value of k is

f:R->R is defined by {:(f(x),=(cos3x-cosx)/(x^2),",","for" x != 0),(,=k, ",","for" x = 0):} If f(x) is continuous at x = 0, the value of k is

If f(x) = {((sin3x)/(x), x !=0),(k/2,x=0):} is continuous at x = 0, then the value of k is

If f(x) = {(kx^(2),"if"x le 2),(3,"if" x gt 2):} is continuous at x = 2, then the value of k is