vazelinahS

2021-10-12

Find the limits

$\underset{x\to \mathrm{\infty}}{lim}\sqrt{\frac{8{x}^{2}-3}{2{x}^{2}+x}}$

berggansS

Skilled2021-10-13Added 91 answers

The degree of both numerator and denominator is=2

So we divide numerator and denominator by$x}^{2$

Calculation:

$\underset{x\to \mathrm{\infty}}{lim}\sqrt{\frac{8{x}^{2}-3}{2{x}^{2}+x}}$

$=\underset{x\to \mathrm{\infty}}{lim}\sqrt{\frac{\frac{(8{x}^{2}-3)}{{x}^{2}}}{\frac{(2{x}^{2}+x)}{{x}^{2}}}}$

$=\underset{x\to \mathrm{\infty}}{lim}\sqrt{\frac{(8-\frac{3}{{x}^{2}})}{(2+\frac{1}{x})}}$

$=\sqrt{\frac{(8-0)}{(2+0)}}$

$=\sqrt{\frac{8}{2}}$

$=\sqrt{4}$

$=2$

Answer: 2

So we divide numerator and denominator by

Calculation:

Answer: 2

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function

$f(x,y)={x}^{3}-6xy+8{y}^{3}$ $\frac{1}{\mathrm{sec}(x)}$ in derivative?

What is the derivative of $\mathrm{ln}(x+1)$?

What is the limit of $e}^{-x$ as $x\to \infty$?

What is the derivative of $f\left(x\right)={5}^{\mathrm{ln}x}$?

What is the derivative of $e}^{-2x$?

How to find $lim\frac{{e}^{t}-1}{t}$ as $t\to 0$ using l'Hospital's Rule?

What is the integral of $\sqrt{9-{x}^{2}}$?

What is the derivative of $f\left(x\right)=\mathrm{ln}\left[{x}^{9}{(x+3)}^{6}{({x}^{2}+7)}^{5}\right]$ ?

What Is the common difference or common ratio of the sequence 2, 5, 8, 11...?

How to find the derivative of $y={e}^{5x}$?

How to evaluate the limit $\frac{\mathrm{sin}\left(5x\right)}{x}$ as x approaches 0?

How to find derivatives of parametric functions?

What is the antiderivative of $-5{e}^{x-1}$?

How to evaluate: indefinite integral $\frac{1+x}{1+{x}^{2}}dx$?