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

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

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

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

2

Solution steps

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

Divide by highest denominator power:

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

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

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

x \to 0 lim (1) = 1

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

= 1 + 1

Simplify

= 2

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