Calc. Practice Problems #10 of 16?

Question

Hello. I have just uploded onto Photobucket 16 calculus practice problems, all of which will be of similar content to my eventual final exam. Now, an answer to these questions would be nice, but is not necessary. Instead, I am concerned with and interested in THE METHOD as to how one could arrive to the correct answer, as well as an EXPLANATION as to why each step needs to be performed in relation to the ones that follow. Anybody who can break down and explain the contents of these problems to me in a SIMPLISTIC way would just be amazing in my book. So thank you very much should you decide to help enlighten me, as I appreciate this more then the words in this post could even begin to convey!

Question #10: http://www.i138.photobucket.com/albums/q271/Link3324/math10.jpg

By the way, This is NOT for any kind of required assignment. It is a guide to work from and to understand before the actual test. Any help would be greatly appreciated. THANK YO

Answer 1

L'Hôpital's rule states that
the limit of this type of ratio function is equal to the limit of the ratio of the derivatives

so
lim(x->1)
of
pi*x^(pi-1)/
e*x^(e-1)
or about 5.44
It really works

j

Answer 2

my fellow yahoo answer member
first plug in the limit value: you will get 0/0
that means that the above limit test in inconclusive meaning there could be an answer or there couldn't be.
take the derivitive of the top: d/dx(x^pi-1)=pi*x^(pi-1)
take the derivitive of the bottom: d/dx(x^e-1)=e*(x*(e-1))
so you get lim as x goes to 1 of pi*x^(pi-1)/e*(x*(e-1))
put in x=1 you will get pi/e which is the answer
the above method was inventer by Lhaspitall
i hope this helps and good luck on your test

Answer 3

#10// l’hopital: pi*x^(pi-1) / (e*x^(e-1)) = (pi/e)*x^(pi-e) =pi/e;