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

The limit as x approaches 0 of (3sin(x)+x)/x is 4

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

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

4

Solution steps

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

Expand

\frac{3 sin ( x ) + x}{x} : \frac{3 sin ( x )}{x} + 1

= x \to 0 lim (\frac{3 sin ( x )}{x} + 1)

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{3 sin ( x )}{x}) + x \to 0 lim (1)

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

x \to 0 lim (1) = 1

= 3 + 1

Simplify

= 4

\int \frac{1}{3 x ( 5 + x )} d x

y = x^{4} + 7 e^{x}, (0, 7)

x \to 2 - lim (H (x))

\frac{d}{d x} (x (2 x + 9)^{\frac{1}{3}})

\int_{0}^{\infty} t e^{- k t} d t

What is the limit as x approaches 0 of (3sin(x)+x)/x ?
The limit as x approaches 0 of (3sin(x)+x)/x is 4