I want to solve:

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

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

cdsommegolfzp
2022-07-09
Answered

I want to solve:

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

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

You can still ask an expert for help

Wade Atkinson

Answered 2022-07-10
Author has **12** answers

The limit is x. The sequence can be squeezed between ${a}_{n}=\frac{x{10}^{n}}{{10}^{n}}=x$ above and ${b}_{n}=\frac{x{10}^{n}-1}{{10}^{n}}$ below. Both limits are equal to x.

asked 2022-06-26

Determine the value of a so that the

$\underset{x\to \mathrm{\infty}}{lim}{({a}^{\frac{1}{x}}+\frac{1}{x})}^{x}=3$

$\underset{x\to \mathrm{\infty}}{lim}{({a}^{\frac{1}{x}}+\frac{1}{x})}^{x}=3$

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Evaluate the limit $\underset{h\Rightarrow 0}{lim}\frac{{(x-h)}^{3}-{x}^{3}}{h}$

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Calculating $\underset{x\to \frac{\pi}{6}}{lim}\left(\frac{\mathrm{sin}(x-\frac{\pi}{6})}{\frac{\sqrt{3}}{2}-\mathrm{cos}x}\right)$, without using L'Hospital rule

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What is the correct solution for the limit $\underset{x\to \mathrm{\infty}}{lim}x\mathrm{sin}\frac{1}{x}$?

asked 2022-07-04

I have to calculate the following limit

$\underset{x\to +\mathrm{\infty}}{lim}\frac{x\mathrm{ln}x}{1-\mathrm{sin}x}$

$\underset{x\to +\mathrm{\infty}}{lim}\frac{x\mathrm{ln}x}{1-\mathrm{sin}x}$

asked 2022-06-09

$\mathrm{arctan}\left(\frac{1}{3}\right)+\mathrm{arctan}\left(\frac{1}{7}\right)+\mathrm{arctan}\left(\frac{1}{13}\right)+\mathrm{arctan}\left(\frac{1}{21}\right)+\cdots $

Estimate the value of the expression if $n\to \mathrm{\infty}$, how to derive this and what will be the approach of this kind of question ?

I have tried to solve this by first doing partial sums then taking limit but I can't evaluate this after getting the form $({n}^{2}+n+1)$

Estimate the value of the expression if $n\to \mathrm{\infty}$, how to derive this and what will be the approach of this kind of question ?

I have tried to solve this by first doing partial sums then taking limit but I can't evaluate this after getting the form $({n}^{2}+n+1)$

asked 2022-08-05

Guess the value of the limit ( it it exists) by evaluationg the funciton at the given numbers ( correct to six decimal places)

a) $lim{x}^{2}-2x/{x}^{2}-x-2,x=2.5,2.1,2.05,2.01,2.005,2.001,1.9,1.95,199,1.995,1.999$

$x\to 2$

b) $lim{x}^{2}-2x/{x}^{2}-x-2,x=0,-0.5,-0.9,-0.95,-0.99,-0.999,-2,-1.5,-1.1,-1.01,-1.001$

$x\to -1$

a) $lim{x}^{2}-2x/{x}^{2}-x-2,x=2.5,2.1,2.05,2.01,2.005,2.001,1.9,1.95,199,1.995,1.999$

$x\to 2$

b) $lim{x}^{2}-2x/{x}^{2}-x-2,x=0,-0.5,-0.9,-0.95,-0.99,-0.999,-2,-1.5,-1.1,-1.01,-1.001$

$x\to -1$