# Questions tagged [calculus-and-analysis]

Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

4,921 questions
Filter by
Sorted by
Tagged with
106 views

### Why does Area produce finite values for this area? [closed]

Let us consider in 13.3.1 on Windows 10 the region reg = ImplicitRegion[{x*y >= 8, y >= 8 x^3, y <= 27}, {x, y}]; and its area ...
21 views

### The relationship between dependent decision variables in a function

Given objective function f(x1,x2,x3) in a optimization problem, and don't know if all these variables are independent or not. How to know if dx2/dx3 is greater/less than/equal to zero. I could
1 vote
252 views

### How to interpolate an implicit function?

chi(t) is implicit function. The implicit function can be plotted by ContourPlot. Is it possible to obtain chi(t) explicitly using function interpolation? ...
91 views

### Why doesn't NMinimize work with NSolve?

Why does NMinimize throw the error and how to fix it? ...
1 vote
120 views

### Gaussian integral not converging

I have a large Gaussian integral to evaluate, and Mathematica claims it does not converge: ...
153 views

### Accuracy of numerical solutions provided by pdetoode

I am interested in solving the following differential equation using pdetoode (you can find pdetoode here). ...
56 views

### Help with limit without using Taylor series [closed]

I would like help solving the following limit: $\lim_{x \rightarrow 0} \frac{x^6 - \arctan(x^6)}{(x - \sin(x))^6}$, but I do not want to use Taylor series. It would be nice to have an answer that does ...
1 vote
113 views

### Can the Debye functions be implemented using built-in functions?

It is claimed in the comments here that the Debye functions can be implemented using built-in special functions. This is clearly true for some Debye functions, e.g., $D_n^{(1)}(x)$ for $n = 1, 2, 3$ (...
105 views

### Plot the surface $xy+z=1$, plane $x+y+z=1,$, and their curve of intersection in different colors

Plot the surface $x y + z = 1$, plane $x+y+z=1$, and their curve of in intersection in different colors.
163 views

### Sierpinski Triangle and Benford's Law (Edit)

I would like some help solving the following problem using Mathematica: Show that, no matter what the initial area of an equilateral triangle is, the sequence of areas (painted in black) of the ...
93 views

### Finding the maximum of a equation

Hi guys I have the following function $R_t = \exp(-2 k_x^2 \sin^2(\frac{t}{2})) k_x^2 \theta(t) \bigg[ -\sin(2t) - \sin(t) (1 - k_x^2 \sin^2(t)) \bigg]$ and I want to find the maximum value of it. I ...
1 vote
133 views

### How to calculate the depth of the lake in mathematica?

I want to calculate mean depth of Goose lake (mean depth=4.6 m), I use bellow command for this operation, But this command is not automatic and we have to create the coordinates manually, and on the ...
64 views

### How to give conditions and solve an integration? [closed]

I want to solve an integration, $\int \frac{da}{\sqrt{\frac{8 \pi G \Lambda}{3}a^2 - K +c_1 a^{-(3k+1)}}}$ Here, how to give conditions k $\ge$ 0, G$>$ 0, $\Lambda$ $>$ 0 and K can be zero, ...
94 views

### Dirac Delta does not converge

I have trouble evaluating a simple integral in Mathematica. I have the code: ...
1 vote
136 views

### Mathematica gives wrong answer to integral of $\ln(x^x)$ [closed]

I want to calculate $\int \ln\left(x^x\right) \, \mathrm{d}x$. It seems that the result is wrong since integrating first and then taking derivative, the result should be the original function, but it'...
102 views

### How do I find the derivative of y^n=x? [closed]

impartial differentiation. I have already logged both side and gotten to nln(y)=ln(x) then differentiated, but then it just turns into a mess and the last place I got to was y(1-xln(y))/(xn)
214 views

1 vote