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Simplify $1+\frac{1}{1+\frac{1}{1+\frac{1}{4+\frac{1}{4}}}}$

Used Formulas

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Solution

Formulas

Videos

Basic Derivatives

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

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
$\frac{d}{dx}\left(\cos\left(\theta \right)\right)=-\sin\left(\theta \right)$

Similar Problems Solved

$\left(-9\right)-\left(-4\right)$

$\left(-9\right)-\left(-6\right)$

$8-\left(-1\right)$

$-5-9$

$3-\left(-6\right)$

$-1+3$

$-7-3$

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 (7)

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