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

The limit as x approaches 0 of 1+(sin(2x))/x is 3

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limit as x approaches 0 of 1+(sin(2x))/x

x \to 0 lim (1 + \frac{sin ( 2 x )}{x})

3

Solution steps

x \to 0 lim (1 + \frac{sin ( 2 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{sin ( 2 x )}{x})

x \to 0 lim (1) = 1

x \to 0 lim (\frac{sin ( 2 x )}{x}) = 2

= 1 + 2

Simplify

= 3

x \to \infty lim (\frac{1}{e x})

x \to 1 lim (\frac{x ^{3}}{x})

x \to \frac{1}{2} lim (0)

x \to 0 lim (x^{17 x})

x \to - 2 lim (f (x) (x)^{2} (x) - x^{2})

What is the limit as x approaches 0 of 1+(sin(2x))/x ?
The limit as x approaches 0 of 1+(sin(2x))/x is 3