What is the limit as x approaches 0+of (x^2+1)/x ?

The limit as x approaches 0+of (x^2+1)/x is infinity

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limit as x approaches 0+of (x^2+1)/x

x \to 0 + lim (\frac{x ^{2} + 1}{x})

\infty

Solution steps

x \to 0 + lim (\frac{x ^{2} + 1}{x})

Divide by highest denominator power:

x + \frac{1}{x}

= x \to 0 + lim (x + \frac{1}{x})

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 0 + lim (x) + x \to 0 + lim (\frac{1}{x})

x \to 0 + lim (x) = 0

x \to 0 + lim (\frac{1}{x}) = \infty

= 0 + \infty

Apply Infinity Property:

c + \infty = \infty

= \infty

x \to 2 lim (\frac{1}{x ^{2} - 9})

y^{^{''}} + 15 y = 0

\frac{d}{d x} (f (x) (x)^{g (x)})

\frac{d}{d x} (\frac{( x + 1 ) ( 2 x - 5 )}{2 x + 3})

\frac{\partial}{\partial y} (sin (3 x + 2 y))

What is the limit as x approaches 0+of (x^2+1)/x ?
The limit as x approaches 0+of (x^2+1)/x is infinity