What is the limit as x approaches 0+of xln(x^7) ?

The limit as x approaches 0+of xln(x^7) is 0

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limit as x approaches 0+of xln(x^7)

x \to 0 + lim (x ln (x^{7}))

0

Solution steps

x \to 0 + lim (x ln (x^{7}))

ln (x^{7}) = 7 ln (x)

= x \to 0 + lim (x \cdot 7 ln (x))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 7 \cdot x \to 0 + lim (x ln (x))

Rewrite for L'Hopital

= 7 \cdot x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})

Apply L'Hopital's Rule

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

= 7 \cdot x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}})

Simplify

\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}} : - x

= 7 \cdot x \to 0 + lim (- x)

Plug in the value

x = 0

= 7 (- 0)

Simplify

= 0

\int x x - 7 d x

\frac{\partial}{\partial x} (sin (- 2 x + 4 y + z))

\frac{d}{d x} (e^{x} sin (x))

\int (\frac{10}{x} + 10 x) d x

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

What is the limit as x approaches 0+of xln(x^7) ?
The limit as x approaches 0+of xln(x^7) is 0