In each of the following, find the value of the constant k so that the given function is continuous at the indicated point :

Question

In each of the following, find the value of the constant k so that the given function is continuous at the indicated point : at x = 0

Philoid · Accepted Answer

Given:

f(x) is continuous at x = 0 & f(0) = 8

If f(x) to be continuous at x = 0,then,

f(0)^– ₌ f(0) ^{+ =} f(0)

LHL = f(0)^– =

cos(–x) = cosx

cos2x = 1–2sin²x

1–cos2x = 2sin²x

2k²

Since f(x) is continuous at x = 0 & f(0) = 8,then

2 k² = 8

⇒ k² = 4

⇒ k = ±2