What is the limit as x approaches 0+of xtan(pi/2-x) ?

The limit as x approaches 0+of xtan(pi/2-x) is 1

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limit as x approaches 0+of xtan(pi/2-x)

x \to 0 + lim (x tan (\frac{π}{2} - x))

1

Solution steps

x \to 0 + lim (x tan (\frac{π}{2} - x))

Rewrite for L'Hopital

= x \to 0 + lim \frac{x}{\frac{1}{t a n ( \frac{π}{2} - x )}}

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 1

x \to 0 lim ((1 - sin (3 x))^{\frac{1}{2 x}})

x \to 4 + lim (x^{2} + 5 x - 35)

x \to \infty lim (3 (x))

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

x \to \infty lim (\frac{x}{a})

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