Nishil Savla

2022-03-29

Show that f(x)=1/x does not have extreme values in interval (0,1).

star233

Skilled2022-06-09Added 352 answers

Find where the expression $\frac{1}{x}$ is undefined.

$x=0$

Consider the rational function $R\left(x\right)=\frac{a{x}^{n}}{b{x}^{m}}$ where n$n$ is the degree of the numerator and $m$ is the degree of the denominator.

1. If $n<m$, then the x-axis, $y=0$, is the horizontal asymptote.

2. If $n=m$, then the horizontal asymptote is the line $y=\frac{a}{b}$.

3. If $n>m$, then there is no horizontal asymptote (there is an oblique asymptote).

Find $n$ and $m$.

$n=0$

$m=1$

Since $n<m$, the x-axis, $y=0$, is the horizontal asymptote.

$y=0$

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

This is the set of all asymptotes.

Vertical Asymptotes: $x=0$

Horizontal Asymptotes: $y=0$

No Oblique Asymptotes

What is the derivative of the work function?

How to use implicit differentiation to find $\frac{dy}{dx}$ given $3{x}^{2}+3{y}^{2}=2$?

How to differentiate $y=\mathrm{log}{x}^{2}$?

The solution of a differential equation y′′+3y′+2y=0 is of the form

A) ${c}_{1}{e}^{x}+{c}_{2}{e}^{2x}$

B) ${c}_{1}{e}^{-x}+{c}_{2}{e}^{3x}$

C) ${c}_{1}{e}^{-x}+{c}_{2}{e}^{-2x}$

D) ${c}_{1}{e}^{-2x}+{c}_{2}{2}^{-x}$How to find instantaneous velocity from a position vs. time graph?

How to implicitly differentiate $\sqrt{xy}=x-2y$?

What is 2xy differentiated implicitly?

How to find the sum of the infinite geometric series given $1+\frac{2}{3}+\frac{4}{9}+...$?

Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?

A. 4.2

B. 4.4

C. 4.7

D. 5.1What is the derivative of $\frac{x+1}{y}$?

How to find the sum of the infinite geometric series 0.9 + 0.09 + 0.009 +…?

How to find the volume of a cone using an integral?

What is the surface area of the solid created by revolving $f\left(x\right)={e}^{2-x},x\in [1,2]$ around the x axis?

How to differentiate ${x}^{\frac{2}{3}}+{y}^{\frac{2}{3}}=4$?

The differential coefficient of $\mathrm{sec}\left({\mathrm{tan}}^{-1}\left(x\right)\right)$.