What is the limit as x approaches 0 of (sin(x^5))/x ?

The limit as x approaches 0 of (sin(x^5))/x is 0

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limit as x approaches 0 of (sin(x^5))/x

x \to 0 lim (\frac{sin ( x ^{5} )}{x})

0

Solution steps

x \to 0 lim (\frac{sin ( x ^{5} )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( x ^{5} ) \cdot 5 x ^{4}}{1})

= x \to 0 lim (\frac{cos ( x ^{5} ) \cdot 5 x ^{4}}{1})

Plug in the value

x = 0

= \frac{cos ( 0 ^{5} ) \cdot 5 \cdot 0 ^{4}}{1}

Simplify

\frac{cos ( 0 ^{5} ) \cdot 5 \cdot 0 ^{4}}{1} : 0

= 0

\int \frac{1}{1 + 9 x ^{2}} d x

\frac{- 3 e ^{(- s 2)}}{( s ^{2} - 5 s + 6 )}

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

ln (x + 8 + x^{2})

\frac{1}{2 x ^{2}}

What is the limit as x approaches 0 of (sin(x^5))/x ?
The limit as x approaches 0 of (sin(x^5))/x is 0