Continuity and Differentiability · Mathematics · Class 12

The function $$f(x)=[x]$$, where $$[x]$$ denotes the greatest integer less than or equal to $$x$$, is continuous at:

If $$x=A \cos 4 t+B \sin 4 t$$, then $$\frac{d^2 x}{d t^2}$$ is equal to:

(a) If $$f(x)=\left\{\begin{array}{ll}x^2, & \text { if } x \geq 1 \\ x, & \text { if } x OR (b) Find the value(s) of '$$\lambda$$', if the function $...

(a) Differentiate $$\quad \sec ^{-1}\left(\frac{1}{\sqrt{1-x^2}}\right) \quad$$ w.r.t. $$\sin ^{-1}\left(2 x \sqrt{1-x^2}\right)$$. OR (b) If $$y=\tan...