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Algebra Baldor
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Find the limit of $\frac{7x^2}{x-x^3}$ as $x$ approaches $\infty $

Used Formulas

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Solution

Formulas

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Basic Derivatives

· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$
· Derivative of a Constant
$\frac{d}{dx}\left(c\right)=0$
· Sum Rule for Differentiation
$\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]=\frac{d}{dx}f\left(x\right) + \frac{d}{dx}g\left(x\right)$
$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
· Power rule for derivatives
$\frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}$

Function Plot

Plotting: $\frac{7x^2}{x-x^3}$

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$\lim_{x\to0}\left(\frac{x^2}{1-cos\left(x\right)}\right)$

Main Topic: Limits to Infinity

The limit of a function f(x) when x tends to infinity is the value that the function takes as the value of x grows indefinitely.

Used Formulas

See formulas (5)

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