Solve Infinite Limit Problems: 2-x/(x-1)^2 & e^x/(x-5)^3

[montana111]

Homework Statement

the book says "find the infinite limit", but it says "lim as x --> 1 of 2-x/(x-1)^2
I don't understand this or how to find the answer. if it was an infinite limit, shouldn't it say as x approaches infinity? The back of my text says the answer is infinity but i don't know how to do the problem still. please help. I am expecting this stuff to be on my quiz this week

Homework Equations

lim as x --> 1 of 2-x/(x-1)^2

and

lim as x --> -3^- of e^x/(x-5)^3

The Attempt at a Solution

i started to make up numbers and factor our things but nothing worked. i got -1/1 from that for the first problem. i have no idea for the second one.

 

[skeptic2]

"infinite limit" sounds like an oxymoron to me.

Why don't you try plugging some numbers into the first example such as .9, .99, .999 or 1.1, 1.01, 1.001. Do you see f(x) approaching a limit?

 

[Mark44]

For your first problem, as x approaches 1 from either side, the numerator approaches 1 (I'm assuming you meant (2 - x)/(x - 1)^2 but left off parentheses in the numerator), and the denominator approaches 0. As a result, the function grows large without bound.

A "limit at infinity" is one where the variable approaches infinity or negative infinity, and the resulting limit can be finite, infinte, or not exist.

For your second problem, is there a typo? As you have written it, the limit can be obtained by evaluating the function at -3.