What is the limit as t approaches 0 of 5tcot(2t) ?

The limit as t approaches 0 of 5tcot(2t) is 5/2

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limit as t approaches 0 of 5tcot(2t)

t \to 0 lim (5 t cot (2 t))

\frac{5}{2}

Decimal Notation

2.5

Solution steps

t \to 0 lim (5 t cot (2 t))

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

= 5 \cdot t \to 0 lim (t cot (2 t))

Rewrite for L'Hopital

= 5 \cdot t \to 0 lim (\frac{t}{\frac{1}{c o t ( 2 t )}})

Apply L'Hopital's Rule

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

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

Plug in the value

t = 0

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

Simplify

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

= \frac{5}{2}

\frac{e ^{- π s}}{s ^{2} + 1}

y = \frac{4 x}{( x ^{2} + 1 )}

\int \frac{2}{9 x ^{2} - 1} d x

\frac{d}{d x} (3 + sin (2 x))

x^{2} - 4 x, 2 x

What is the limit as t approaches 0 of 5tcot(2t) ?
The limit as t approaches 0 of 5tcot(2t) is 5/2