Compute the following limits

Question

a) limx→1 1 / x − 1=

(b) lim x→1+ x + 2 / x − 1=

(c) lim x→∞ 2x / x − 5 =

(d) lim x→−∞ 5x² − 6x³ / 7x⁴ + 2x − 9 —=

Answer 1

a) Taking the left limit as x→1^- is -∞, right limit is ∞, so the limit does not exist

b)lim x→1⁺ (x+1)/(x-1) = lim x→1⁺ (x+1) • lim x→1⁺ 1/(x-1) =2•∞ = ∞

c) 2x/(x-5) = 2/(1-5/x)

lim x→∞ 2/(1-5/x) = 2/(1-5/∞) = 2/(1-0) = 2

d) (5x² − 6x³) / (7x⁴ + 2x − 9) = (5/x²-6/x)/(7+2/x³-9/x⁴)

lim x→∞(5/x²-6/x)/(7+2/x³-9/x⁴) = (0-0)/(7+0-0) = 0