Question

If \( f(x) = \frac{x}{1 + x^2} + \frac{x}{(1 + x^2)^2} + \cdots \) to infinity, then at \( x = 0, f(x) \)

• A. has no limit
• B. is discontinuous
• C. is continuous but not differentiable
• D. is differentiable

Hint:

Examine the behavior of the terms in an infinite series at specific values of \( x \) to determine if the series is continuous or differentiable.

Answer 1

The Correct Option is B

At \( x = 0 \), the function behaves discontinuously due to the powers of \( x^2 \). Therefore, the function is not continuous and is not differentiable.