Calculus and Limits

Question

[5 pts] For each part below, give possible formulas for two functions f(x) and g(x) that

satisfy the given condition.

(a) lim x-->1 f(x)/g(x) = 0

(b) lim x-->1 f(x)/g(x) = 1

(c) lim x-->1 f(x)/g(x) = does not exist

Answer 1

There are infinite possible combinations.

Here you are three examples that satisfy the given conditions

a) f(x)=x-1

g(x)=x+5

b) f(x)=e^x-1

g(x)=x

c) f(x)=|x-1| (absolute value of x-1)

g(x)=x-1

Best,

Davide