SOLUTION: Let {{{f(x)=(x^2(x-1)(5x^2+3x-4))/(2x^5-3x^4+4x^3-5x^2)}}} Find: a. lim f(n) as n-->-Infinity b. lim f(n) as n-->-1 c. lim f(n) as n-->0

Algebra ->  Rational-functions -> SOLUTION: Let {{{f(x)=(x^2(x-1)(5x^2+3x-4))/(2x^5-3x^4+4x^3-5x^2)}}} Find: a. lim f(n) as n-->-Infinity b. lim f(n) as n-->-1 c. lim f(n) as n-->0      Log On


   

Question 1035838: Let f%28x%29=%28x%5E2%28x-1%29%285x%5E2%2B3x-4%29%29%2F%282x%5E5-3x%5E4%2B4x%5E3-5x%5E2%29
Find:
a. lim f(n) as n-->-Infinity
b. lim f(n) as n-->-1
c. lim f(n) as n-->0
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a. Suppose x+%3C%3E+0. Then x%5E2 can be cancelled from top and bottom, and the numerator is a polynomial in which the leading term is 5x%5E3, while the denominator is a polynomial with a leading term of 2x%5E3. Therefore as n goes to infinity, f(n) goes to 5/2.
b. As n approaches -1, f(n) approaches -2/7. (In fact f(x) is continuous at x = -1).
c. Returning to the argument used in (a), in any neighborhood of x = 0, f(x) is defined except at x = 0 itself. This means the limit, as n approaches 0, would be -4/5. (There is a removable discontinuity at x = 0.)