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

The limit as x approaches 0 of (sin(3x))/x+2 is 5

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

x \to 0 lim (\frac{sin ( 3 x )}{x} + 2)

5

Solution steps

x \to 0 lim (\frac{sin ( 3 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 ( 3 x )}{x}) + x \to 0 lim (2)

x \to 0 lim (\frac{sin ( 3 x )}{x}) = 3

x \to 0 lim (2) = 2

= 3 + 2

Simplify

= 5

\frac{1}{x ^{4}} \frac{d y}{d x} = 19 + 15 y

\frac{d ^{2}}{d x ^{2}} (t^{3} (e)^{3 t})

\int (t^{2} + 1) e^{- 2 t} d t

y = 4 sin (x) cos (x), at x = \frac{π}{4}

4 x^{2} + 4 x + x y = 4

What is the limit as x approaches 0 of (sin(3x))/x+2 ?
The limit as x approaches 0 of (sin(3x))/x+2 is 5