What is the limit as x approaches 3 of 1/((x-3)^8) ?

The limit as x approaches 3 of 1/((x-3)^8) is infinity

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limit as x approaches 3 of 1/((x-3)^8)

x \to 3 lim (\frac{1}{( x - 3 ) ^{8}})

\infty

Solution steps

x \to 3 lim (\frac{1}{( x - 3 ) ^{8}})

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 3 - lim (\frac{1}{( x - 3 ) ^{8}}) = \infty

x \to 3 + lim (\frac{1}{( x - 3 ) ^{8}}) = \infty

= \infty

x sin (\frac{3}{x})

x \to - 3 lim (\frac{x ^{2} - 9}{3 + x})

\frac{d}{d x} (\frac{2}{3 x ^{\frac{1}{3}}})

\int_{3}^{5} \frac{x}{x ^{2} - 3} d x

(6 x^{2} - 10 x) e^{x}

What is the limit as x approaches 3 of 1/((x-3)^8) ?
The limit as x approaches 3 of 1/((x-3)^8) is infinity