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

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

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

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

\infty

Solution steps

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

x \to 0 + lim (csc (x)) = \infty

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

= \infty + \infty

Apply Infinity Property:

\infty + \infty = \infty

= \infty

x \to 4 lim (ln (x))

x \to 8 lim (\frac{7}{x - 8})

x \to - 2 lim (1 + x^{3})

x \to - \infty lim (3 x^{5})

x \to 0 lim ((1 + 4 x)^{\frac{2}{x}})

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