What is the limit as x approaches 0 of 1+(tan(x))/x ?

The limit as x approaches 0 of 1+(tan(x))/x is 2

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limit as x approaches 0 of 1+(tan(x))/x

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

2

Solution steps

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

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

x \to 0 lim (1) = 1

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

= 1 + 1

Simplify

= 2

x \to - 1 lim ([x] + [- x])

x \to 0 lim (\frac{x ^{2} - 5 x}{x ^{2} + 8 x})

x \to - 2 - lim (\frac{x ^{2} + 1}{x + 2})

x \to - \infty lim (\frac{x}{0})

x \to 0 lim (arccot (x))

What is the limit as x approaches 0 of 1+(tan(x))/x ?
The limit as x approaches 0 of 1+(tan(x))/x is 2