What is the limit as x approaches 1 of (x^{-2}-6^{-2})/(x+6) ?

The limit as x approaches 1 of (x^{-2}-6^{-2})/(x+6) is 5/36

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limit as x approaches 1 of (x^{-2}-6^{-2})/(x+6)

x \to 1 lim (\frac{x ^{- 2} - 6 ^{- 2}}{x + 6})

\frac{5}{36}

Decimal Notation

0.13888 \dots

Solution steps

x \to 1 lim (\frac{x ^{- 2} - 6 ^{- 2}}{x + 6})

Plug in the value

x = 1

= \frac{1 ^{- 2} - 6 ^{- 2}}{1 + 6}

Simplify

\frac{1 ^{- 2} - 6 ^{- 2}}{1 + 6} : \frac{5}{36}

= \frac{5}{36}

\int e^{(- 3 x)} d x

\int_{0}^{1} (x^{6} + x^{8}) d x

\frac{d y}{d x} + 4 x y = x e^{x^{2}}

x^{2} \cdot e^{x}

x \to - 5 lim (\frac{3 x + 8}{x + 5})

What is the limit as x approaches 1 of (x^{-2}-6^{-2})/(x+6) ?
The limit as x approaches 1 of (x^{-2}-6^{-2})/(x+6) is 5/36