What is the limit as x approaches 0 of (sin(2x))/x+4 ?

The limit as x approaches 0 of (sin(2x))/x+4 is 6

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limit as x approaches 0 of (sin(2x))/x+4

x \to 0 lim (\frac{sin ( 2 x )}{x} + 4)

6

Solution steps

x \to 0 lim (\frac{sin ( 2 x )}{x} + 4)

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 (4)

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

x \to 0 lim (4) = 4

= 2 + 4

Simplify

= 6

\frac{d}{d x} ((2 x^{2} - 4 x)^{\frac{1}{2}})

x \to \infty lim (x^{2} + 3)

\int_{0}^{12} 3 x d x

f (t) = 2 cos (2 t)

What is the limit as x approaches 0 of (sin(2x))/x+4 ?
The limit as x approaches 0 of (sin(2x))/x+4 is 6