CBSE (Science) Class 12CBSE
Share
Notifications

View all notifications

Examine the Continuity of F, Where F is Defined by F(X) = {(Sin X - Cos X, If X != 0),(-1,If X = 0) - CBSE (Science) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

Examine the continuity of f, where f is defined by

`f(x) = {(sin x - cos x, if x != 0),(-1, "," if x = 0):}`

Solution

The given function f is `f(x) = {(sin x - cos x, if x != 0),(-1, "," if x = 0):}`

It is evident that f is defined at all points of the real line.

Let c be a real number.

Case I:

Therefore, f is continuous at all points x, such that x ≠ 0

Case II:

Therefore, f is continuous at x = 0

From the above observations, it can be concluded that f is continuous at every point of the real line.

Thus, f is a continuous function.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 5: Continuity and Differentiability
Q: 25 | Page no. 161
Solution Examine the Continuity of F, Where F is Defined by F(X) = {(Sin X - Cos X, If X != 0),(-1,If X = 0) Concept: Concept of Continuity.
S
View in app×