What is the limit as x approaches 5 of x/((x-5)^4) ?

The limit as x approaches 5 of x/((x-5)^4) is infinity

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limit as x approaches 5 of x/((x-5)^4)

x \to 5 lim (\frac{x}{( x - 5 ) ^{4}})

\infty

Solution steps

x \to 5 lim (\frac{x}{( x - 5 ) ^{4}})

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

then

x \to a lim f (x) = L

x \to 5 - lim (\frac{x}{( x - 5 ) ^{4}}) = \infty

x \to 5 + lim (\frac{x}{( x - 5 ) ^{4}}) = \infty

= \infty

What is the limit as x approaches 5 of x/((x-5)^4) ?
The limit as x approaches 5 of x/((x-5)^4) is infinity