What is the limit as x approaches 0 of 7cot^4(3x) ?

The limit as x approaches 0 of 7cot^4(3x) is infinity

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limit as x approaches 0 of 7cot^4(3x)

x \to 0 lim (7 cot^{4} (3 x))

\infty

Solution steps

x \to 0 lim (7 cot^{4} (3 x))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 7 \cdot x \to 0 lim (cot^{4} (3 x))

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= 7 (x \to 0 lim (cot (3 x)))^{4}

Apply the Limit Chain Rule:

\infty

= 7 \infty^{4}

Simplify

7 \infty^{4} : \infty

= \infty

\int \frac{cos ( x )}{x} d x

f (x) = 5 (7 + x)

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

x \to 1 - lim (x)

\int 2 x^{9} e^{- x^{5}} d x

What is the limit as x approaches 0 of 7cot^4(3x) ?
The limit as x approaches 0 of 7cot^4(3x) is infinity