The value of lim_{x -> 1} (x^7 - 2x^5 + 1) / (x^3 - 3x^2 + 2) is A. is 0 B. is -1 C. is 1 D. does not exist

GATE 2017 · Engineering Mathematics · Limits · medium

Answer: 1

1. Check indeterminate form: Substituting x = 1: numerator = 1 - 2 + 1 = 0, denominator = 1 - 3 + 2 = 0. This is 0/0 form.
2. Differentiate numerator and denominator: f'(x) = 7x^6 - 10x^4; g'(x) = 3x^2 - 6x. At x = 1: f'(1) = 7 - 10 = -3; g'(1) = 3 - 6 = -3.
3. Compute the limit: The limit equals -3/-3 = 1. Answer is option C.