What is the limit as x approaches 0 of (sin(5x))/x+4 ?

The limit as x approaches 0 of (sin(5x))/x+4 is 9

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limit as x approaches 0 of (sin(5x))/x+4

x \to 0 lim (\frac{sin ( 5 x )}{x} + 4)

9

Solution steps

x \to 0 lim (\frac{sin ( 5 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 ( 5 x )}{x}) + x \to 0 lim (4)

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

x \to 0 lim (4) = 4

= 5 + 4

Simplify

= 9

\int (\frac{e ^{x}}{1 + e ^{2 x}}) d x

\int_{2}^{3} \frac{2 t}{1 + t ^{2}} d t

\int 9 x^{8} d x

\frac{3 x}{5 y}

y = x^{3} + 3

What is the limit as x approaches 0 of (sin(5x))/x+4 ?
The limit as x approaches 0 of (sin(5x))/x+4 is 9