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

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

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

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

6

Solution steps

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

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

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

x \to 0 lim (2) = 2

= 4 + 2

Simplify

= 6

\frac{\partial}{\partial x} (x^{3} + y^{2} - 5 x y)

4 y^{^{''}} - y^{^{'}} = 0

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = 0

\int_{0}^{7} (50 x + 20) d x

\frac{d}{d x} (sin (π x))

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