Evaluate the limit $lim_(h rarr 0) {(x-h)^3-x^3}/h$ ?

Question

Evaluate the limit $lim_(h rarr 0) {(x-h)^3-x^3}/h$ ?

1 Answer

Related questions

What is the limit definition of the derivative of the function $y=f(x)$ ?
Ho do I use the limit definition of derivative to find $f'(x)$ for $f(x)=3x^2+x$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=sqrt(x+3)$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=1/(1-x)$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=x^3-2$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=1/sqrt(x)$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=5x-9x^2$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=sqrt(2+6x)$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=mx+b$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=c$ ?

Impact of this question

30443 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-14T09:54:29

$lim_(h rarr 0) {(x-h)^3-x^3}/h = -3x^2$

Explanation:

We seek:

$L = lim_(h rarr 0) {(x-h)^3-x^3}/h$

Therefore:

$L = lim_(h rarr 0) {x^3-3x^2h+3xh^2-h^3-x^3}/h$
$\ \ \ = lim_(h rarr 0){-3x^2h+3xh^2-h^3}/h$

$\ \ \ = lim_(h rarr 0)-3x^2+3xh-h^2$

$\ \ \ = -3x^2 +0 + 0$

$\ \ \ = -3x^2$

Science

Math

Humanities

... and beyond

Evaluate the limit $lim_(h rarr 0) {(x-h)^3-x^3}/h$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Evaluate the limit lim_(h rarr 0) {(x-h)^3-x^3}/hlim_(h rarr 0) {(x-h)^3-x^3}/h?

1 Answer

Explanation:

Related questions

Impact of this question

Evaluate the limit $lim_(h rarr 0) {(x-h)^3-x^3}/h$ ?