continuity

Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined as follows: $$ f(x)=\left\{\begin{array}{cc} c_1 e^x-c_2 \log _e\left(\frac{1}{x}\right), & \text { if } x>0 \\...

Consider the given function $f(x)$. $$f(x)=\left\{\begin{array}{cc} a x+b & \text { for } x If the function is differentiable everywhere, the value of $b$ must be _________ (Rounde...

Let $$\,\,f\left( x \right) = {x^{ - \left( {1/3} \right)}}\,\,$$ and $${\rm A}$$ denote the area of the region bounded by $$f(x)$$ and the $$X-$$axis, when $$x$$ varies from $$-1$...

Which one of the following functions is continuous at $$x = 3$$?

Which one of the following functions is continuous at $$x=3?$$

Consider the following two statements about the function $$$f\left( x \right) = \left| x \right|:$$$ $$P.\,\,f\left( x \right)$$ is continuous for all real values of $$x$$ $$Q.\,\,...

Consider the function $$y = \left| x \right|$$ in the interval $$\left[ { - 1,1} \right]$$. In this interval, the function is