University:
York University
Course:
MATH 1013 | Applied Calculus I
Academic year:

2022
Views:

221

Pages:

4
Author:

Nick T.

Chapter 2.3 Continuity hole jump vertical asymptote 1. g(1) = 6 lim x→1 [f(x) + g(x)] = 36 3f(1) + f(1) * g(1) = 36 3f(1) + 6f(1) = 36 9f(1) = 36 f(1) = 4 2. g(1) = 5 lim x→1 [f(x) * g(x)] = 24 f(1) * g(1) = 24 5f(1) = 24 f(1) = 24/5 3. f(x) = (x^2 - x - 2) / (x - 2) f(x) = (x - 2)(x + 1) / (x - 2) f(x) = x + 1 4. lim x→49 (√x - 7) / (x - 49) lim x→49 (√x - 7) / (√x - 7)(√x + 7) lim x→49 1 / (√x + 7) 1 / (√49 + 7) 1 / 14 1. 4x + 3 = 0 4x = -3 x = -3/4 (x - 8)(x + 1) (x - 8)(x + 1) 2. lim x→∞ (6x² - x + 4) / (4x² + 5x - 2) (6x² - x + 4) / (4x² + 5x - 2) (6 - 1/x + 4/x²) / (4 + 5/x - 2/x²) 6 / 4 3 / 2 6. lim x→∞ (√(x + 1) - √x) / (x - 1) lim x→∞ (√(x + 1) - √x) / (x - 1) * (√(x + 1) + √x) / (√(x + 1) + √x) lim x→∞ (x + 1 - x) / ((x - 1)(√(x + 1) + √x)) lim x→∞ 1 / ((x - 1)(√(x + 1) + √x)) 1 / ∞ 0 16. lim t→∞ (√(t + 1) - t) / (t - 1) lim t→∞ (√(t + 1) - t) / (t - 1) * (√(t + 1) + t) / (√(t + 1) + t) lim t→∞ (t + 1 - t²) / ((t - 1)(√(t + 1) + t)) lim t→∞ (-t² + t + 1) / ((t - 1)(√(t + 1) + t)) lim t→∞ (-1 + 1/t + 1/t²) / ((1 - 1/t)(√(1 + 1/t) + 1)) -1 / (1 + 1) -1/2 17. lim x→∞ (√(9x² + x) - 3x) / (√(x² + x) - x) (√(9x² + x) - 3x) * (√(9x² + x) + 3x) / (√(x² + x) - x) * (√(x² + x) + x) (9x² + x - 9x²) / (x² + x - x²) x / x 1 18. lim x→∞ (√(x² + ax) - √(x² + bx)) (√(x² + ax) - √(x² + bx)) * (√(x² + ax) + √(x² + bx)) / (√(x² + ax) + √(x² + bx)) (x² + ax - x² - bx) / (√(x² + ax) + √(x² + bx)) (a - b)x / (√(x² + ax) + √(x² + bx)) (a - b) / (√(1 + a/x) + √(1 + b/x)) (a - b) / 2 19. y = (x² - 3) / (x - 1) y = (x - 1)(x + 1) / (x - 1) y = x + 1 (x - 1)(x + 1) / (x - 3)(x - 1) (x + 1) / (x - 3) x + 1 = 0 x = -1 20. y = (x² - x - 6) / (x² - 5x) (x - 3)(x + 2) / x(x - 5) x + 2 = 0 x = -2