What is the limit as x approaches 0 of (sin(5x^2))/x ?

The limit as x approaches 0 of (sin(5x^2))/x is 0

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limit as x approaches 0 of (sin(5x^2))/x

x \to 0 lim (\frac{sin ( 5 x ^{2} )}{x})

0

Solution steps

x \to 0 lim (\frac{sin ( 5 x ^{2} )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 5 x ^{2} ) \cdot 10 x}{1})

= x \to 0 lim (\frac{cos ( 5 x ^{2} ) \cdot 10 x}{1})

Plug in the value

x = 0

= \frac{cos ( 5 \cdot 0 ^{2} ) \cdot 10 \cdot 0}{1}

Simplify

\frac{cos ( 5 \cdot 0 ^{2} ) \cdot 10 \cdot 0}{1} : 0

= 0

x \to 1 + lim (\frac{1}{x ^{2}})

x \to 1 lim (cos (\frac{1}{x}))

x \to \infty lim (+ x - (+ x))

x \to e - lim (\frac{2}{ln ( x ) - 1})

x \to - 5 lim (- 13)

What is the limit as x approaches 0 of (sin(5x^2))/x ?
The limit as x approaches 0 of (sin(5x^2))/x is 0