What is the limit as x approaches 0 of (sin(x^4))/x ?

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

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limit as x approaches 0 of (sin(x^4))/x

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

0

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( x ^{4} ) \cdot 4 x ^{3}}{1})

= x \to 0 lim (\frac{cos ( x ^{4} ) \cdot 4 x ^{3}}{1})

Plug in the value

x = 0

= \frac{cos ( 0 ^{4} ) \cdot 4 \cdot 0 ^{3}}{1}

Simplify

\frac{cos ( 0 ^{4} ) \cdot 4 \cdot 0 ^{3}}{1} : 0

= 0

10

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\int \frac{1}{x ^{2} + 9 x + 20} d x

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