# Questions tagged [calculus]

For basic questions about limits, derivatives, integrals and applications, mainly of one-variable functions.

94,876 questions
Filter by
Sorted by
Tagged with
25 views

22 views

### Example of a function that is non-differentiable on an open interval

I am studying a course on single variable calculus. During a lecture, the professor mentioned in passing that there can be functions that are non-differentiable on an entire open interval. Can anyone ...
34 views

### Integrals Definite substitution from this? [on hold]

Integrals Definite substitution from $$\int^{\pi/4}_{0}\frac{8 \cos(2t)}{\sqrt {9-5 \sin t (2t)}}~dt ~?$$? u = 9 - 5 sin t(2t) du = -10(t cos (t) + sin (t)) , this correct for du = -10(t cos (t) ...
55 views

70 views

### Find two continuous functions such that $\int_1^\infty f(x) dx$ and $\int_1^\infty g(x) dx$ converge but $\int_1^\infty f(x)g(x) dx$ diverge

Since $\int_1^\infty f(x)\,dx$ and $\int_1^\infty g(x) \,dx$ are converge, $\lim_{x\to\infty}f(x)=0$ and $\lim_{x\to\infty}g(x)=0$, so $f,g$ are fractional function, and denominator is changing more ...
### Trying to understand the following proof of $f(x) = a^x \implies f'(x) = a^x \ln a$
I was reading proof of how to obtain derivative of $a^x$ here (Click on the screenshot below to expand). Although I comprehend the proof, I have several questions about the way the proof is ...