What is the limit as x approaches 0 of (3x^2+5cos(x)-5)/(2x) ?

The limit as x approaches 0 of (3x^2+5cos(x)-5)/(2x) is 0

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limit as x approaches 0 of (3x^2+5cos(x)-5)/(2x)

x \to 0 lim (\frac{3 x ^{2} + 5 cos ( x ) - 5}{2 x})

0

Solution steps

x \to 0 lim (\frac{3 x ^{2} + 5 cos ( x ) - 5}{2 x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{2} \cdot x \to 0 lim (\frac{3 x ^{2} + 5 cos ( x ) - 5}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{6 x - 5 sin ( x )}{1})

= \frac{1}{2} \cdot x \to 0 lim (\frac{6 x - 5 sin ( x )}{1})

Plug in the value

x = 0

= \frac{1}{2} \cdot \frac{6 \cdot 0 - 5 sin ( 0 )}{1}

Simplify

\frac{1}{2} \cdot \frac{6 \cdot 0 - 5 sin ( 0 )}{1} : 0

= 0

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θ \to 0 lim ((1 - sin^{2} (θ))^{\frac{1}{2}})

x \to 0 lim (x cos (\frac{15}{x}))

What is the limit as x approaches 0 of (3x^2+5cos(x)-5)/(2x) ?
The limit as x approaches 0 of (3x^2+5cos(x)-5)/(2x) is 0