Continuity

A function defined as f(x) = \frac{1 - \cos 4x}{x^2} for x \neq 0 and f(0) = m is continuous; find m...

For the greatest integer function, at how many points in the open interval (0,3) is g(x) = [x] + [-x...

Suppose f(x) = \frac{\sqrt{1+x} - \sqrt{1-x}}{x} for x \neq 0 and f(0) = k; which k makes f continuo...

Given the piecewise function shown, with f(x)=ax+1 for x \le 2 and f(x)=bx-3 for x>2, find a relatio...

Let $f:[0,1]\to \mathbb{R}$ be continuous, $f(0)=0,f(1)=1$. Which of the following is guaranteed b...

Let $f(x)=[x{]}^2+\sqrt{\{x\}}$, where $[.]$ denotes the greatest integer function and $\{.\}$ den...

If f(x) = {(x² - 4)/(x - 2) for x ≠ 2; k for x = 2} is continuous at x = 2, then k equals

Evaluate \lim_{x \to 0} \frac{x - \sin x}{x - \tan x}, a ratio of two third-order vanishing trigonom...

Using L'Hopital's rule or expansion, the limit \lim_{x \to 0} \frac{e^x - 1 - x}{x^2} evaluates to w...

Define f(x) = x^2 for x \le 1 and f(x) = ax + b for x > 1; find a, b making f differentiable everywh...

Assertion: every differentiable function is continuous. Reason: differentiability requires the diffe...

If y = x^x for x > 0, then the derivative dy/dx evaluated through logarithmic differentiation equals...