What is the limit as x approaches 0 of 5xcot(x) ?

The limit as x approaches 0 of 5xcot(x) is 5

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limit as x approaches 0 of 5xcot(x)

x \to 0 lim (5 x cot (x))

5

Solution steps

x \to 0 lim (5 x cot (x))

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

= 5 \cdot x \to 0 lim (x cot (x))

Rewrite for L'Hopital

= 5 \cdot x \to 0 lim (\frac{x}{\frac{1}{c o t ( x )}})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{sec ^{2} ( x )})

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

Plug in the value

x = 0

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

Simplify

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

= 5

x \to 3 lim (\frac{x - 1}{6 - 2 x})

x \to 2 lim (3 x^{2} - 4 x)

x \to 8 lim (2 x \cdot 2 x)

x \to 0 + lim (3 tan (x) ln (x))

x \to 5 lim (x + 10)

What is the limit as x approaches 0 of 5xcot(x) ?
The limit as x approaches 0 of 5xcot(x) is 5