What is the limit as x approaches 0 of x^2cot(4x^2) ?

The limit as x approaches 0 of x^2cot(4x^2) is 1/4

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limit as x approaches 0 of x^2cot(4x^2)

x \to 0 lim (x^{2} cot (4 x^{2}))

\frac{1}{4}

Decimal

0.25

Solution steps

x \to 0 lim (x^{2} cot (4 x^{2}))

Rewrite for L'Hopital

= x \to 0 lim (\frac{x ^{2}}{\frac{1}{c o t ( 4 x ^{2} )}})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{2 x}{sec ^{2} ( 4 x ^{2} ) \cdot 8 x})

= x \to 0 lim (\frac{2 x}{sec ^{2} ( 4 x ^{2} ) \cdot 8 x})

Simplify

\frac{2 x}{sec ^{2} ( 4 x ^{2} ) \cdot 8 x} : \frac{1}{4} cos^{2} (4 x^{2})

= x \to 0 lim (\frac{1}{4} cos^{2} (4 x^{2}))

Plug in the value

x = 0

= \frac{1}{4} cos^{2} (4 \cdot 0^{2})

Simplify

\frac{1}{4} cos^{2} (4 \cdot 0^{2}) : \frac{1}{4}

= \frac{1}{4}

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

x \to 3 lim (\frac{e ^{x}}{x - 3})

x \to 3 + lim (x + 6)

x \to - 4 - lim (\frac{x + 5}{x + 4})

x \to - \infty lim (\frac{3 x ^{2} + 6}{5 - 2 x})

What is the limit as x approaches 0 of x^2cot(4x^2) ?
The limit as x approaches 0 of x^2cot(4x^2) is 1/4