Hello, i've got some questions i really don't know how to prove/solve, and thats limits of infinity involving fraction as exponents.(lim x->+infinity (x)^(2/ln(1+x^3)) ) .
here are some questions that puzzles me on:
pi = the "pi" sign
sqrt. of = sqrt. of a number
infinity = infinity sign
1.) lim x->+infinity (x)^(2/ln(1+x^3))
2.) lim x->0^+ (cos sqrt of x)^(1/x)
3.) limx->1-0 ((2/pi)(arcsin(x)))^(1/acrcos(x))
4.) lim x->0^+ (x)^((1)/(1+ln sqrt. of x))
5.) lim x->+infinity (2+e^x)^(-1/x)
6.) lim x->0 (1+3x)^(2/sin(x))
7.) lim x->0 ((a^x+b^x+c^x)/(3))^(1/x)
well, I've already encounter and solve some limits but not related on these parts(fractions as exponents)
tried reading my book but didn't show some examples on how to solve it.
If you know how to solve it, please let me know.
or if you've got some examples,then show it to me.
thanks for your time!
anyway mind to check if my answers for no.2,4, and 5 are correct
in no. 2 I get an answer of -0.5 ; no.4 e^2 ; no.5 -1
while i'm still tryingto solve 3,6,7