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

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

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

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

3

Solution steps

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

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

x \to 0 lim (1) = 1

= 2 + 1

Simplify

= 3

x \to 0 + lim (x sin (\frac{1}{5 x}))

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

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

x \to 0 lim ((\frac{a ^{x} + b ^{x}}{2})^{\frac{1}{x}})

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