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

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

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limit as x approaches 0 of 2(1/x-cot(x))

x \to 0 lim (2 (\frac{1}{x} - cot (x)))

0

Solution steps

x \to 0 lim (2 (\frac{1}{x} - cot (x)))

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 0 - lim (2 (\frac{1}{x} - cot (x))) = 0

x \to 0 + lim (2 (\frac{1}{x} - cot (x))) = 0

= 0

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

x \to 0 lim (π coth (\frac{1}{x}))

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

t \to 0 lim (\frac{5 ^{t} - 1}{t})

x \to 2 lim (\frac{x + 1}{4 - x ^{2}})

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