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Algebra Baldor
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Find the limit of $\frac{\ln\left(x\right)^2}{x-1}$ as $x$ approaches $1$

Used Formulas

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Solution

Formulas

Videos

Basic Derivatives

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

Function Plot

Plotting: $\frac{\ln\left(x\right)^2}{x-1}$

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Find the limit

$\lim_{x\to0}\left(\frac{\cos\left(5x\right)-1}{x^2}\right)$

Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

Used Formulas

See formulas (4)

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