limit of $x/\mathrm{sin}(\pi x)$ as x approaches zero?

varitero5w
2022-06-24
Answered

limit of $x/\mathrm{sin}(\pi x)$ as x approaches zero?

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Eleanor Luna

Answered 2022-06-25
Author has **19** answers

hint: $\frac{x}{\mathrm{sin}(\pi x)}}={\displaystyle \frac{1}{\pi}}\cdot {\displaystyle \frac{\pi x}{\mathrm{sin}(\pi x)}$

doodverft05

Answered 2022-06-26
Author has **2** answers

Hint: Show L'Hopital's Rule applies and write

$\underset{x\to 0}{lim}\frac{x}{\mathrm{sin}(\pi x)}=\underset{x\to 0}{lim}\frac{1}{\pi \mathrm{cos}(\pi x)}$

$\underset{x\to 0}{lim}\frac{x}{\mathrm{sin}(\pi x)}=\underset{x\to 0}{lim}\frac{1}{\pi \mathrm{cos}(\pi x)}$

asked 2021-06-08

Use the limit definition of the derivative to calculate the derivatives of the following function:

(a)$f(x)=4{x}^{2}+3x+1$

(b)$f(x)=\frac{2}{{x}^{2}}$

(a)

(b)

asked 2022-07-08

How to evaluate $\underset{n\to \mathrm{\infty}}{lim}\left({\int}_{0}^{2\pi}\frac{\mathrm{cos}(nx)}{{x}^{2}+{n}^{2}}dx\right)where\text{}\mathrm{\forall}\text{}\text{}n\in \mathbb{N}$

asked 2021-09-11

Use the limit definition of the derivative to calculate the derivatives of the following function:

(a)$f\left(x\right)=4{x}^{2}+3x+1$

(b)$f\left(x\right)=\frac{2}{{x}^{2}}$

(a)

(b)

asked 2022-07-04

Trigonometric Limit without L'hospital (0/0 kind): $\underset{x\to \frac{\pi}{6}}{lim}\text{}\frac{\mathrm{sin}(x-\frac{\pi}{6})}{\frac{\sqrt{3}}{2}-\mathrm{cos}(x)}$

asked 2022-06-16

Calculate

$\underset{x\to \pi /2}{lim}\frac{\mathrm{cos}x}{x-\frac{\pi}{2}}$

by relating it to a value of $(\mathrm{cos}x{)}^{\prime}$

$\underset{x\to \pi /2}{lim}\frac{\mathrm{cos}x}{x-\frac{\pi}{2}}$

by relating it to a value of $(\mathrm{cos}x{)}^{\prime}$

asked 2022-06-05

Find the sum of the series:

$\underset{n\to \mathrm{\infty}}{lim}\frac{\mathrm{sin}1}{1}+\frac{\mathrm{sin}2}{2}+\frac{\mathrm{sin}3}{3}+...+\frac{\mathrm{sin}n}{n}$

I have no clue how to find this.

$\underset{n\to \mathrm{\infty}}{lim}\frac{\mathrm{sin}1}{1}+\frac{\mathrm{sin}2}{2}+\frac{\mathrm{sin}3}{3}+...+\frac{\mathrm{sin}n}{n}$

I have no clue how to find this.

asked 2022-07-09

I want to solve:

$\underset{n\to \mathrm{\infty}}{lim}\frac{floor(x\cdot {10}^{n})}{{10}^{n}}$

$\underset{n\to \mathrm{\infty}}{lim}\frac{floor(x\cdot {10}^{n})}{{10}^{n}}$