What is the limit $lim_{x \to 0} \frac{1 - c o s ( 4 x )}{x ^{2}}$ ?

Practise more Limits, Continuity and Global Theorems.

Free questions with an explanation for every one, and full timed Panhellenic Examinations (Greece) mock tests.

All Limits, Continuity and Global Theorems questions Take a mock test

More Limits, Continuity and Global Theorems questions

What is the value of $lim_{x \to 0} \frac{s i n ( 5 x )}{t a n ( 2 x )}$ ?
What is the limit $lim_{x \to + \infty} (x^{2} + 6 x - x)$ ?
Let $f : [1, 5] \to R$ be continuous with $f (1) = - 3$ and $f (5) = 7$ . Which statement is guaranteed by Bolzano's theorem?
What is the horizontal asymptote of the function $f (x) = \frac{4 e ^{x} + 3}{2 e ^{x} + 5}$ as $x \to + \infty$ ?
If $f$ is continuous on $[0, 4]$ with $f (0) = 2$ and $f (4) = 10$ , which theorem guarantees a value $c \in (0, 4)$ where $f (c) = 6$ ?
What is the vertical asymptote of $f (x) = \frac{x ^{2} - 9}{x ^{2} - 5 x + 6}$ ?