$\lim_{x \to 0^+} x^{9x}$

Calculus Level 1

Evaluate $\lim_{x \to 0^+} x^{9x}.$

\frac{1}{9}

e

1 0

2 solutions

Vidya Shirur
Mar 22, 2014

derivation of x^9x is 9x.lnx+1 so lim ->0+ Answer is 1

Arijit Banerjee
Mar 3, 2014

Take ln on both sides then on RHS write the exp as 9 * (ln x)/(1/x) and now apply L hospital and then it comes -9x now put the limits and remove ln u will get e^0 = 1.

lim ⁡ x → 0 + x 9 x \lim_{x \to 0^+} x^{9x} lim x → 0 + ​ x 9 x

2 solutions

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$\lim_{x \to 0^+} x^{9x}$