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

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

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

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

2

Solution steps

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

Divide by highest denominator power:

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

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

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

x \to 0 lim (1) = 1

= 1 + 1

Simplify

= 2

x \to 0 lim (- \frac{1}{∣ x ∣})

x \to 1 - lim (ln (ln (x)))

x \to 0 lim ((12 + x)^{x})

x \to - 1 lim (3 x + 2)

x \to 1 lim (\frac{1}{( 1 - x ) ^{2}})

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