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

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

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

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

4

Solution steps

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

Divide by highest denominator power:

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

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

x \to 0 lim (3) = 3

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

= 3 + 1

Simplify

= 4

x \to \infty lim (\frac{8}{3})

t \to 0 + lim (t ln (t^{2}))

x \to 0 lim (5 x ln (x))

x \to 0 lim (\frac{1}{( x - 1 ) ^{4} + 2})

x \to - \infty lim (x + e^{x})

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