Answer to Question #1955 in Calculus for Vigi

Question

Evaluate the limit.

lim x->0^+ (9x+1)^cot(x)

Answer 1

<img src="/cgi-bin/mimetex.cgi?%5Clim_%7Bx%20%5Cto%200%5E+%7D%289x+1%29%5E%7B%5Ccot%7Bx%7D%7D%20=%5Clim_%7Bx%20%5Cto%200%5E+%7D%289x+1%29%5E%7B1/x%7D%20=%5Clim_%7Bx%20%5Cto%200%5E+%7D%28%289x+1%29%5E%7B1/9x%7D%29%20%5E9%20=%20e%5E9" title="\lim_{x \to 0^+}(9x+1)^{\cot{x}} =\lim_{x \to 0^+}(9x+1)^{1/x} =\lim_{x \to 0^+}((9x+1)^{1/9x}) ^9 = e^9">