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

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

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limit as x approaches 0+of sin(x)+1/x

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

\infty

Solution steps

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

x \to 0 + lim (sin (x)) = 0

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

= 0 + \infty

Apply Infinity Property:

c + \infty = \infty

= \infty

x \to 0 + lim (x^{e^{x} - 1})

x \to 8 lim ((89 + 4 x))

x \to 5 + lim (x - 5)

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

x \to 0 lim ((cos (x))^{x})

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