What is the limit as x approaches 7+of 1/((x-7)^2)+1 ?

The limit as x approaches 7+of 1/((x-7)^2)+1 is infinity

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limit as x approaches 7+of 1/((x-7)^2)+1

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

\infty

Solution steps

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

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

With the exception of indeterminate form

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

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

x \to 7 + lim (1) = 1

= \infty + 1

Apply Infinity Property:

\infty + c = \infty

= \infty

x \to 1 lim (5 x)

x \to 0 + lim (sin^{2 x} (x))

x \to 0 lim (x + 2 - 1)

x \to - \infty lim (x + 2)

x \to - 2 lim (\frac{4 x ^{2}}{x + 2})

What is the limit as x approaches 7+of 1/((x-7)^2)+1 ?
The limit as x approaches 7+of 1/((x-7)^2)+1 is infinity