What is the limit as x approaches 0 of (4-4cos(x))/(x^2) ?

The limit as x approaches 0 of (4-4cos(x))/(x^2) is 2

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limit as x approaches 0 of (4-4cos(x))/(x^2)

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

2

Solution steps

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

Apply L'Hopital's Rule

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{4 cos ( 0 )}{2}

Simplify

\frac{4 cos ( 0 )}{2} : 2

= 2

x \to 0 lim (\frac{2 ∣ x ∣}{2 x})

h \to 0 lim (\frac{7 ^{h} - 1}{h})

x \to 3 lim (\frac{5 x}{4} + 3)

t \to \infty lim (3^{- t})

x \to 4 lim ([4 f (x) - 5 g (x)])

What is the limit as x approaches 0 of (4-4cos(x))/(x^2) ?
The limit as x approaches 0 of (4-4cos(x))/(x^2) is 2