# calculus's questions - Chinese 1answer

82.604 calculus questions.

### For which $p>0$ does $\sum_{n=3}^{\infty}\frac{\log(n)}{n^p}$ converge?

For which $p>0$ does $\sum_{n=3}^{\infty}\frac{\log(n)}{n^p}$ converge? I tried all the criteria for series convergence I know, but I'm not getting any further with this exercise. I'm not asking ...

### Recurrence relation with periodic function

3 answers, 430 views calculus recurrence-relations
$$x_{n+1} = x_n + \sin x_n$$ $$x_{n+1} = \sin \left(\frac {\pi} {2} x_n\right)$$ How to solve these? Or, at least, what can be said about their behavior and limits?

### $\lim_{n \to \infty}\frac{1}{n}\int^{b+\frac{1}{n}}_{b} F(x)dx=F(b)$

0 answers, 7 views calculus real-analysis

### Calculus - Find the position and velocity of an object when it hits the ground - using vector

1 answers, 30 views calculus vectors projectile-motion
If an object is thrown in the air with an initial position of $(0,0,4)$ in feet and initial velocity $(200,0,256)$ in feet per second, and the acceleration is $(0,8,-32)$. Find the position and ...

### 1 Product of three binomials

Suppose you have a product of three binomials each of which can be represented as binomial series: $(1-x)^{\frac{1}{2}}\times (1+4x)^{\frac{1}{2}}\times (1-2x)^{-2}$ How do you find the center and ...

### 6 How to calculate the integral $\int_{0.5}^{1} \frac{1}{\sqrt{2x-x^2}}$?

3 answers, 137 views calculus integration trigonometry
I have the following integration problem: $$\int_{0.5}^{1} \frac{1}{\sqrt{2x-x^2}}$$ And I can see I should probably be completing the square here. I may be missing something extremely obvious, ...

### Can a continuous function have discontinuities?

3 answers, 64 views calculus continuity
$f(x) = \frac{1}{x}$ The function is supposedly continuous, but there is an infinite discontinuity at $x = 0$. I'm confused. Isn't the definition of a continuous function as one that doesn't have ...