What is the limit as x approaches 5-of (x^2+7)/(x^2-25) ?

The limit as x approaches 5-of (x^2+7)/(x^2-25) is -infinity

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limit as x approaches 5-of (x^2+7)/(x^2-25)

x \to 5 - lim (\frac{x ^{2} + 7}{x ^{2} - 25})

- \infty

Solution steps

x \to 5 - lim (\frac{x ^{2} + 7}{x ^{2} - 25})

\frac{x ^{2} + 7}{x ^{2} - 25} = (x^{2} + 7) \frac{1}{x ^{2} - 25}

= x \to 5 - lim ((x^{2} + 7) \frac{1}{x ^{2} - 25})

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

With the exception of indeterminate form

= x \to 5 - lim (x^{2} + 7) \cdot x \to 5 - lim (\frac{1}{x ^{2} - 25})

x \to 5 - lim (x^{2} + 7) = 32

x \to 5 - lim (\frac{1}{x ^{2} - 25}) = - \infty

= 32 (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

x \to 0 lim ((e^{x} - x)^{\frac{3}{x}})

x \to - \frac{π}{2} lim (- 7 x - \frac{π}{2})

x \to 1 lim (\frac{x - 1}{x ^{2} - 8 x + 7})

x \to \infty lim (x \cdot (e^{0 x} - 1))

2 \to 10 lim (2^{2} + 4)

What is the limit as x approaches 5-of (x^2+7)/(x^2-25) ?
The limit as x approaches 5-of (x^2+7)/(x^2-25) is -infinity