Evaluate the limit: lim x---> -2
x^2-x-6/x+2
This is one of my review questions for my test, having a hard time understanding limits, could someone solve and explain please??
x^2-x-6/x+2
This is one of my review questions for my test, having a hard time understanding limits, could someone solve and explain please??
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Hi Chelsea,
There are a few ways to approach this problem. I am going to approach it the way I believe your instructor would like to see it.
Your first approach would be simply plugging the number in, but you soon realize that it is undefined. At a second glance you notice that the numerator can be factored. You can get that to (x-3)(x+2). Now you have
Limit as x approaches -2
[ (x-3) (x+2) ] / (x+2)
You can cancel out the (x+2)'s leading to the limit as x approaches -2
(x-3)
You can now simply plug in the -2, (-2 - 3) = -5.
So your final answer is -5. I will assume you understand what that answers means. If you don't, just let me know.
There are a few ways to approach this problem. I am going to approach it the way I believe your instructor would like to see it.
Your first approach would be simply plugging the number in, but you soon realize that it is undefined. At a second glance you notice that the numerator can be factored. You can get that to (x-3)(x+2). Now you have
Limit as x approaches -2
[ (x-3) (x+2) ] / (x+2)
You can cancel out the (x+2)'s leading to the limit as x approaches -2
(x-3)
You can now simply plug in the -2, (-2 - 3) = -5.
So your final answer is -5. I will assume you understand what that answers means. If you don't, just let me know.
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Let L = limit
L = (x^2 - x - 6) / (x+2)
L = (x+2)(x-3) / (x+2) = x-3
L = -5 as x approaches -2
L = (x^2 - x - 6) / (x+2)
L = (x+2)(x-3) / (x+2) = x-3
L = -5 as x approaches -2