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 2

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

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

2

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

= 2

x \to 0 lim (x^{8} cos (\frac{1}{x}))

x \to 0 lim (tan (x) - x)

y \to 3 lim (\frac{y ^{3} - 13 y + 12}{y ^{3} - 14 y + 15})

x \to 0 lim (\frac{tan ( 4 x )}{2 x})

x \to - 7 lim (\frac{4 x - 1}{x + 7})

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 2