f(x) = {1 if x<1, x if 1<x} and g(x) = {x if x is not equal to 2, 3 if x=2}

Question

Please help ASAP. Thanks!

Answer 1

(a) f(0)=1 because x<1 and g(0)=0 because x≠2 so the limit for g(x)/f(x)=g(0)/f(0)=0/1=0.

(b) f(2)=2 because x>1 and g(2)=3 because x=2 so the limit is f(2)/g(2)=2/3.

Comments

But when i answer your answer on my assignment it says that it was partially correct. Only the letter (a) is correct while the letter (b) is wrong. Please answer and by the way, all of your answers are great sir.

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Yes, you’re right, I was fooled! When x➝2 it’s not actually equal to 2. So g(2)=2 not 3 and the limit is 1 not 2/3. Sorry about that. I wasn’t thinking straight! The quotient is x/x=1, because f(x) and g(x) both equal x when x=2.

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Thank you sir, it was correct.