Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.

# Questions tagged [calculus]

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

97,637 questions
Filter by
Sorted by
Tagged with
8 views

22 views

### Show that a function is negative over its domain

I would like to demonstrate that the following function is negative \begin{equation} -\frac{t}{4\sqrt{x}^3}\bigg[1-\bigg(1+\sqrt{x}\bigg)^{\frac{1}{t-1}}\bigg]+\bigg(\frac{1}{1-t}\bigg)\bigg(\frac{t}{...
26 views

### Singularity of holomorphic function

Let $f: \mathbb C \rightarrow \mathbb C$ be a holomorphic function in an open set around some $c \in \mathbb C$, but excluding $c$. Moreover, assume that the Laurent series for $f$ around $c$ ...
42 views

43 views

I've figured out that the repeated limit exists: $$\lim_{m \to \infty} \lim_{n \to \infty} \cos^{2n}(m! \pi x) = \begin{cases} 1,&x\text{ is rational}\\ 0,&x\text{ is irrational}\end{cases} ... 2answers 29 views ### finding coordinates with derivatives Find the coordinates of the point on the curve x^2+xy+y^2=7 where the slope is the same as at the point (2,1). I’ve already found y’ to be \frac{(-2x+y)}{(x+2y)} and the slope at the point ... 1answer 18 views ### Lagrange multiplier volume maximatisation Using method of lagrange multiplier show that among all rectangular parallelepiped inscribed in a given sphere cube has the maximum volume 2answers 60 views ### Setting up the volume \iiint_{?}^{?}dV Let$$S = \{ (x,y,z) | x=a+b, y = b+c, z = -b, ac-b^2\ge0, c\ge0, a\ge0\}$$and$$x^2+y^2+z^2\le 1$$Compute the volume of S. My work:$$V=\iiint_R 1 dV = \int\limits_{-1}^{1}\int\limits_{-\sqrt{(1-...
I think there are 10 unknowns. $$A_y,A_x,B_y,B_x,C_x,C_y,D_x,D_y,E_x,T$$ And unable to obtain 10 equations so uanble to solve this question. The answer is 138 lb according to the book for the ...