# Tagged Questions

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

0answers
110 views

### Why Can't Mathematica Integrate this? [closed]

I am trying to integrate Absolute-value functions from Wikipedia: ...
4answers
245 views

### Results in terms of a function

Let's assume I have a function $f(x)=\exp(10x^2)$, i.e. f[x_]:= Exp[10*x^2]. When I differentiate $f$ by evaluating the expression ...
1answer
134 views

### Differential Equations and Unit Notation

What do I get the Syntax::sntxi: Incomplete expression; more input is needed . error when I try to use the math palette for derivatives? What does the dot in ...
2answers
208 views

### Use Meijer-G function to represent elementary functions

I want to represent these elementary functions: $x^{2}\sqrt{x}$, $\sin{4x}$, and $x\ln{x}$ as cases of MeijerG. What arguments should I give to ...
1answer
64 views

### Taylor and Maclaurin series [closed]

I need to calculate limit of sin(x)*cot(tanx) at 0 using Maclaurin series I took the usual approach but did not get anything of help.
3answers
225 views

### Limit n->Infinity of recursive sequence

I have defined a recursive sequence a[0] := 1 a[n_] := Sqrt[3] + 1/2 a[n - 1] because I want to calculate the Limit for this ...
5answers
167 views

### How to find the derivative value at $(\pi,0)$ for this implicit function $n$ times?

I am trying to take the implicit derivative at $\sin(x+y)+\sin(x)=y$ and substitute $x=\pi$ and $y=0$ at least 6-7 times since I need to find the Taylor series for this function. Since I barely ...
0answers
79 views

### How to evaluate this integral

I am trying to evaluate the following integral in Mathematica: ...
1answer
56 views

### Same integral gives different results with assumption

b = 1 k = 12560 r = 500 res = Integrate[Exp[I*k*x*Sin[o]]/(r + x*Sin[o]), {x, -b/2, b/2}] resab = Abs[res]^2 Plot[resab, {o, -Pi/20, Pi/20}, PlotRange -> Full] ...
1answer
122 views

### DensityPlot showing artifacts [closed]

This is my first post on Mathematica.SE, and I'm still a bit new to Mathematica. I believe I'm probably doing something silly in my code, but I have not been able to find where. I'm trying to plot a ...
0answers
90 views

### Inconsistent results for symbolic trigonometric integral

I am trying to evaluate (on Mathematica v.9) the integral $$\int_0^x [\sin (x) \sin (2 y)-\sin (2 x) \sin (y)]^t \,\mathrm{d}y,$$ where $t$ is an even, positive integer. ...
0answers
95 views

1answer
132 views

### Integrating differential solid angle over the unit hemisphere

When reading about rendering topics I commonly run into integrals over a hemisphere similar to this one: $\int_\Omega n \cdot l \, d\omega$ If I want to put that in Mathematica then I can re-...
1answer
105 views

### Solving this equation with NDSolve

I'm trying to solve a differential equation numerically. I've written this code but it is leading to some errors "initial history needs to be specified for all variables for delay-differential ...
2answers
59 views

### Why i cannot get a numerical result? [closed]

I have tried following code: Limit[((sinx)^6)/(cosx - e^(-(x^(2))/2) + (x^(4))/12), x -> 0] Following is the image representing what I have tried to implement:...
0answers
95 views

### Integrate dealing with Sqrt gives wrong answers

I often find when I integrate something with a Sqrt[x] term in it, Mathematica gives an incorrect result. I assume this must be due to some kind of incorrect ...
3answers
115 views

### How to typeset and evaluate $u \big|_a^b$

Sometimes I need to evaluate an expression at the end points. e.g. the right hand side of $\int_a^bf(x)\textrm{d}x=F(x)\big|_a^b$. $F(x)$ could be complex at the right hand side so I can't just ...
2answers
99 views

### Using Mathematica to find the areas described by polar curves

I am working on a project and I need to find the area of the surface inside the polar-curve $r=2\cos(\theta)$ and outside the polar-curve $r=1$. The graph is pretty straightforward: just two ...