Math help

[Rahminator]

My math teacher handed out a take home test which I almost finished, save for 2 problems. If you feel like helping a brother out, here they are:

If P(x) and Q(x) are two polynomial functions in x such that lim [x->a] P(x)/Q(x) = P(a)/Q(a), then which of the following statements must be true?
A) a is not a root of the equation P(x) = 0
B) a is not a root of the equation Q(x) = 0
C) a must be a root of the equation P(x) = 0 or Q(x) = 0
D) a != 0
E) a is a root of the equation P(x) = Q(x)

Which of the following functions fails to satisfy the conclusion of the Mean Value Theorem on the given interval?
A) f(x) = 3x^2 - 2x on [0, 1]
B) f(x) = x^-2 on [-1, 2]
C) f(x) = x^(2/3) on [1, 2]
D) f(x) = ln x on [e, 2e]
E) f(x) = e^x on [1, 3]

I really appreciate your help.

 

[Zorro]

I had Tuna Tataki for dinner.

 

[rgwalt]

Originally posted by: Rahminator
My math teacher handed out a take home test which I almost finished, save for 2 problems. If you feel like helping a brother out, here they are:

If P(x) and Q(x) are two polynomial functions in x such that lim [x->a] P(x)/Q(x) = P(a)/Q(a), then which of the following statements must be true?
A) a is not a root of the equation P(x) = 0
B) a is not a root of the equation Q(x) = 0
C) a must be a root of the equation P(x) = 0 or Q(x) = 0
D) a != 0
E) a is a root of the equation P(x) = Q(x)

Which of the following functions fails to satisfy the conclusion of the Mean Value Theorem on the given interval?
A) f(x) = 3x^2 - 2x on [0, 1]
B) f(x) = x^-2 on [-1, 2]
C) f(x) = x^(2/3) on [1, 2]
D) f(x) = ln x on [e, 2e]
E) f(x) = e^x on [1, 3]

I really appreciate your help.

w/o breaking out my old math books, I think the answer to the first question is B. If a is a root of Q(x), then the limit would be undefined.

Ryan

 

[Rahminator]

*bump*

anyone?

 

[chiwawa626]

Its a test, its supposed to test your knowledge.

Minus 4 chiwawa626 points for you.