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

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

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

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

- \frac{1}{π}

Decimal Notation

- 0.31830 \dots

Solution steps

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

Plug in the value

x = 0

= \frac{0 + π sec ( 0 )}{0 ^{2} - π ^{2}}

Simplify

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

= - \frac{1}{π}

x \to 0 lim (3 x)

z \to 0 lim (\frac{∣ x ∣ - z}{z})

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

x \to - \infty lim (x^{3} - 4 x)

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

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