PYQs Based Test - 03 : Limits, Continuity and Differentiability

The values of x for which the function

$f\left(x\right)=\frac{x^2-3x-4}{x^2+3x-4}$

is NOT continuous are

Given the following statements about a function f: R → R, select the right option:

P: If f(x) is continuous at x = x₀, then it is also differentiable at x = x0.

Q: If f(x) is continuous at x = x0, then it may not be differentiable at x = x0.

R: If f(x) is differentiable at x = x0, then it is also continuous at x = x0.

The value of $\underset{x\to 0}{\lim }\frac{1-\cos \left(x^2\right)}{2x^4}$ is

What should be the value of λ such that the function defined below is continuous at x = π/2?

≤ft( ) = ≤ft\{ {*20c {{{λ }}{{{π }2 - }}}&{≠ {π }2}\\ 1&{= {π }2} } .