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If f(x)={((tanx)/(sinx)",", x ne 0),(1",...

If `f(x)={((tanx)/(sinx)",", x ne 0),(1",", x =0):}` then f(x) is

A

continuous everywhere

B

continuous no where

C

continuous at x = 0

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `f(x)={((tanx)/(sin x)",", x ne 0) , ( 1",", x =0):}`
`rArr lim_( x to 0) f(x) =lim_( x to 0) (tan x)/(sin x)=lim_( x to 0) ((tanx)/(x))/((sin x)/(x))`
`=(1)/(1) =1=f(0)`
Hence, f(x) is continuous at x = 0
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  6. Which of the following functions is continuous at x = 0 ?

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  14. Let f(x)={((cos^(2)x-sin^(2)x-1)/(sqrt(x^(2)+4)-2)"," , x ne 0),(a",",...

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  15. Let f(x)={(1-cos4x)/(x^2),\ \ \ if\ x<0a ,\ \ \ if\ x=0(sqrt(x))/(sqrt...

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