What is the limit as x approaches-pi of (x+pi)cot(x) ?

The limit as x approaches-pi of (x+pi)cot(x) is 1

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limit as x approaches-pi of (x+pi)cot(x)

x \to - π lim ((x + π) cot (x))

1

Solution steps

x \to - π lim ((x + π) cot (x))

Rewrite for L'Hopital

= x \to - π lim (\frac{x + π}{\frac{1}{c o t ( x )}})

Apply L'Hopital's Rule

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

= x \to - π lim (\frac{1}{sec ^{2} ( x )})

Plug in the value

x = - π

= \frac{1}{sec ^{2} ( - π )}

Simplify

\frac{1}{sec ^{2} ( - π )} : 1

= 1

\int sin^{7} (y) d y

\int \frac{3}{35} x^{2} d x

y^{^{'''}} + 2 y^{^{''}} - 13 y^{^{'}} + 10 y = 0

y^{^{''}} + 2 y^{^{'}} + 4 y = 0

\int \frac{7}{1 + x ^{2}} d x

What is the limit as x approaches-pi of (x+pi)cot(x) ?
The limit as x approaches-pi of (x+pi)cot(x) is 1