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

The limit as x approaches 0 of (2x+sin(x))/x is 3

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

x \to 0 lim (\frac{2 x + sin ( x )}{x})

3

Solution steps

x \to 0 lim (\frac{2 x + sin ( x )}{x})

Divide by highest denominator power:

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

= x \to 0 lim (2 + \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 (2) + x \to 0 lim (\frac{sin ( x )}{x})

x \to 0 lim (2) = 2

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

= 2 + 1

Simplify

= 3

x \to - 1 lim (- 4 x)

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

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

x \to 0 lim (\frac{6 x}{cot ( x )})

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

What is the limit as x approaches 0 of (2x+sin(x))/x ?
The limit as x approaches 0 of (2x+sin(x))/x is 3