What is the limit as x approaches 0 of (tan(x)+x)/x ?

The limit as x approaches 0 of (tan(x)+x)/x is 2

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limit as x approaches 0 of (tan(x)+x)/x

x \to 0 lim (\frac{tan ( x ) + x}{x})

2

Solution steps

x \to 0 lim (\frac{tan ( x ) + x}{x})

Expand

\frac{tan ( x ) + x}{x} : \frac{tan ( x )}{x} + 1

= x \to 0 lim (\frac{tan ( x )}{x} + 1)

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to 0 lim (\frac{tan ( x )}{x}) + x \to 0 lim (1)

x \to 0 lim (\frac{tan ( x )}{x}) = 1

x \to 0 lim (1) = 1

= 1 + 1

Simplify

= 2

n = 0 \sum \infty 3 (- \frac{1}{4})^{n - 1}

\int 20 e^{x} d x

\frac{d}{d x} (\frac{12}{x ^{4}})

(x, y) \to (0, 0) lim (x y^{8})

\frac{d}{d x} (\frac{1}{x ^{2} + c})

What is the limit as x approaches 0 of (tan(x)+x)/x ?
The limit as x approaches 0 of (tan(x)+x)/x is 2