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

The limit as x approaches e of x(e^x+1/x) is e^{1+e}+1

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limit as x approaches e of x(e^x+1/x)

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

e^{1 + e} + 1

Decimal Notation

42.19355 \dots

Solution steps

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

Plug in the value

x = e

= e (e^{e} + \frac{1}{e})

Simplify

e (e^{e} + \frac{1}{e}) : e^{1 + e} + 1

= e^{1 + e} + 1

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

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

\int (sin (x) + 7 cos (x) - 1) d x

(t e)^{3} e^{- 2 (t + 1)}

n = 5 \sum \infty e^{5 - 2 n}

What is the limit as x approaches e of x(e^x+1/x) ?
The limit as x approaches e of x(e^x+1/x) is e^{1+e}+1