# Questions tagged [calculus]

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

94,864 questions
Filter by
Sorted by
Tagged with
1answer
53 views

### how to find minimum form piecewise function

Equation: $$(1+6.64x)^2+4(1+8.89x)^2-8(1+6.64x)-16(1+8.89x)-(\frac{1}{((1+6.64x)+(1+8.89x)-5)}+\frac{1}{((1+6.64x)-3)}-\frac{1}{(1+6.64x)}-\frac{1}{(1+8.89x)})$$ plot and solution form wolframalpha ...
2answers
46 views

### Approximations using derivatives

I came across the following definitions in my textbook: The differential of $x$, denoted by $dx$, is defined by $dx = \Delta x$ The differential of $y$, denoted by $dy$, is defined by $dy=f'(x) dx$ ...
1answer
32 views

### Please explain this integration relation [closed]

For $a>0,{\ }b>0$, $$\lim_{T\to\infty}\int_{a}^{b}\frac{-e^{-Ty}}{y}\,\mathrm{d}y = \lim_{T\to\infty}\int_{Ta}^{Tb}\frac{-e^{-y}}{y}\,\mathrm{d}y$$
0answers
29 views

1answer
81 views

### Trying to find roots of $\arctan(2(x − 1)) − \ln |x| = 0$ analytically

I have found the roots graphically and also numerically. Apparently there is also a calculus root to finding them analytically. I was thinking to use the derivative but it doesn't seem to work. ...
2answers
52 views

### Splitting $~x~$ and $~y~$ and solving for $~y~$

Solve for $~y~$: $$3xy+5y=2x+7$$ I have to do this for as an assignment going into Calculus, the problem is the teacher wants us to research how to do the problems on our own, and I don't know what ...
1answer
23 views

### Swapping charge time for a capacitor doesn't behave as expected

This is a very basic question about equations but reading online courses about equations didn't clear up what I'm missing. TLDR; How to get from $T = RC$ to $R = \frac{T}{C}$ Working on a Raspberry ...
0answers
32 views

1answer
79 views

4answers
175 views

2answers
132 views

### Is this true for all polynomials

I took $3$ random polynomials with non zero roots one having even degree and two having odd degrees $f(x)=\color{red}{4}x^2-(4\sqrt3+12)x+12\sqrt3$ having roots $\color{blue}{3,\sqrt3}$ and leading ...
3answers
47 views

### What is Jacobian in Vector Calculus? [closed]

What is A Jacobian? How will you explain it in layman language? What are it's applications?