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

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

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

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

0

Solution steps

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

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

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- sec ( x ) tan ( x )}{1})

= \frac{1}{2} \cdot x \to 0 lim (\frac{- sec ( x ) tan ( x )}{1})

Plug in the value

x = 0

= \frac{1}{2} \cdot \frac{- sec ( 0 ) tan ( 0 )}{1}

Simplify

\frac{1}{2} \cdot \frac{- sec ( 0 ) tan ( 0 )}{1} : 0

= 0

x \to 1 lim (\frac{∣ 1 - x ∣}{x - 1})

w \to 0 lim (\frac{cos ( w ) - cos ( 2 w )}{sin ^{2} ( w )})

x \to 0 + lim (x^{2} (ln (x^{2})))

x \to 0 lim (x \frac{1}{x})

x \to 0 lim (tan (x) (ln (x)))

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