The value of k that makes

By Team Aakash Byju's | 30th November 2022 f(x ) = { sin ( ), for x ≠ 0 k, for x = 0 1 x continuous at X = 0 is -1 None 0 1

Detailed Explanation

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We know that, if a function f(x) is continuous at x = 0, then

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Applying the same to the given function we can write

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But

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Trigonometry Values Notes for Math Board Exams Revision

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The value of k that makes

A.

B.

C.

D.

Detailed Explanation

The correct answer is D. None.

We know that, if a function f(x) is continuous at x = 0, then

lim f (x) = f (0)

x

0

Applying the same to the given function we can write

lim sin( ) = k

x

0

=>

1

x

But

lim sin( )

x

0

1

x

Therefore, for any value of k, the given function cannot be continuous at x = 0.

does not exist.

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