What is the limit as x approaches 0 of e^x+3x 1/x ?

The limit as x approaches 0 of e^x+3x 1/x is 4

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limit as x approaches 0 of e^x+3x 1/x

x \to 0 lim (e^{x} + 3 x \frac{1}{x})

4

Solution steps

x \to 0 lim (e^{x} + 3 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 (e^{x}) + x \to 0 lim (3 x \frac{1}{x})

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

x \to 0 lim (3 x \frac{1}{x}) = 3

= 1 + 3

Simplify

= 4

\frac{d}{d t} (4 e^{\frac{t}{2}})

arcsin (6 x + 1)

\frac{d}{d x} (\frac{3}{x - 1})

f (x) = 6 x e^{x} csc (x)

(- 5, 7), (3, - 5)

What is the limit as x approaches 0 of e^x+3x 1/x ?
The limit as x approaches 0 of e^x+3x 1/x is 4