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Algebra Baldor
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Find the limit of $\frac{1}{x}+\frac{-1}{\sin\left(x\right)}$ as $x$ approaches 0

Used Formulas

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Solution

Formulas

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Basic Derivatives

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

Derivatives of trigonometric functions

· Derivative of the sine function
$\frac{d}{dx}\left(\sin\left(\theta \right)\right)=\cos\left(\theta \right)$
· Derivative of the cosine function
$\frac{d}{dx}\left(\cos\left(\theta \right)\right)=-\sin\left(\theta \right)$

Function Plot

Plotting: $\frac{1}{x}+\frac{-1}{\sin\left(x\right)}$

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Main Topic: Limits by L'Hôpital's rule

In mathematics, and more specifically in calculus, L'Hôpital's rule uses derivatives to help evaluate limits involving indeterminate forms.

Used Formulas

See formulas (6)

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