What is the limit as w approaches 0 of (sec(2w)-1)/(wsec(2w)) ?

The limit as w approaches 0 of (sec(2w)-1)/(wsec(2w)) is 0

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limit as w approaches 0 of (sec(2w)-1)/(wsec(2w))

w \to 0 lim (\frac{sec ( 2 w ) - 1}{w sec ( 2 w )})

0

Solution steps

w \to 0 lim (\frac{sec ( 2 w ) - 1}{w sec ( 2 w )})

Apply L'Hopital's Rule

: w \to 0 lim (\frac{2 sec ( 2 w ) tan ( 2 w )}{sec ( 2 w ) + 2 w sec ( 2 w ) tan ( 2 w )})

= w \to 0 lim (\frac{2 sec ( 2 w ) tan ( 2 w )}{sec ( 2 w ) + 2 w sec ( 2 w ) tan ( 2 w )})

Plug in the value

w = 0

= \frac{2 sec ( 2 \cdot 0 ) tan ( 2 \cdot 0 )}{sec ( 2 \cdot 0 ) + 2 \cdot 0 \cdot sec ( 2 \cdot 0 ) tan ( 2 \cdot 0 )}

Simplify

\frac{2 sec ( 2 \cdot 0 ) tan ( 2 \cdot 0 )}{sec ( 2 \cdot 0 ) + 2 \cdot 0 \cdot sec ( 2 \cdot 0 ) tan ( 2 \cdot 0 )} : 0

= 0

y = x, y = 8 - x, y = 0

2 sin (x) + 2 cos (x)

y^{^{'}} = y^{2} sin (x^{2}), y (- 2) = \frac{1}{3}

x \to 0 lim (g (x) (f (x)))

\int_{0}^{1} \frac{e ^{x}}{x} d x

What is the limit as w approaches 0 of (sec(2w)-1)/(wsec(2w)) ?
The limit as w approaches 0 of (sec(2w)-1)/(wsec(2w)) is 0