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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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