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Question

Mathematics Question on Sequence and series

The value of k which makes f(x)={sin⁡x,x≠0k,x=0 continuous at x=0, is:

A

(A) 2

B

(B) 1

C

(C) −1

D

(D) 0

Answer

(D) 0

Explanation

Solution

Explanation:
f(x) is Continuous at x=0⇒limx→0+f(x)=limx→0−f(x)=f(0)⇒limx→0+sin⁡x=limx→0−sin⁡x=k⇒limh→0sin⁡(0+h)=limh→0sin⁡(0−h)=k⇒k=0Hence, the correct option is (B).