What is the limit as x approaches 0 of (sin(x^3))/x ?

The limit as x approaches 0 of (sin(x^3))/x is 0

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

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

0

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( x ^{3} ) \cdot 3 x ^{2}}{1})

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

Plug in the value

x = 0

= \frac{cos ( 0 ^{3} ) \cdot 3 \cdot 0 ^{2}}{1}

Simplify

\frac{cos ( 0 ^{3} ) \cdot 3 \cdot 0 ^{2}}{1} : 0

= 0

\int cos^{7} (x) sin^{6} (x) d x

9 + cot^{2} (x)

x^{2} (1 - 2 x)

(1 - x) \frac{d y}{d x} - x y = x + x^{2}

n = 0 \sum \infty \frac{1}{1.0 1 ^{n}}

What is the limit as x approaches 0 of (sin(x^3))/x ?
The limit as x approaches 0 of (sin(x^3))/x is 0