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

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

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

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

\infty

Solution steps

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

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

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

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

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

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

= 2 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\frac{\partial}{\partial x} (x^{4} + 2 x^{2} y^{2})

8 x^{3} + 2 x + 7 x^{\frac{1}{3}}

\int e^{x} + x e^{x} d x

\frac{d}{d x} ((x^{2} - 2 x) e^{x})

\int x sin (- 3 x) d x

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