Calculus limits help!?

Question

find the limit as x approaches 2: (3x^2+6x)/(x^2-4). i think i got it right but i just want to make sure im doing it correctly and check my answer. its for a summer assignment so its not fresh in my mind. if you could figure this out the help is appreciated! :)

Answer 1

say f(x) = (3x^2+6x)/(x^2-4)

            = [3x*(x+2)]/[(x-2)*(x+2)]

            = 3x/(x-2)

As x approaches 2, the denominator approaches zero, the f(x) approaches infinity.

If the question for limit at x approaches - 2 (which is my guess), then

  f(x) = 3/2 = 1.5

Answer 2

Edit:

The limit is undefined.

The equation can be rewritten as [3x*(x+2)]/[(x+2)*(x-2)]

The x+2 on the top and bottom cancel out, leaving

3x/(x-2)

Evaluate f(x) as x approaches 2 from the right:

f(2.1)=(3*2.1)/.1=63

f(2.01)=(3*2.01)/.01=603

f(2.001)=(3*2.001)/.001=6003

f(2.0001)=(3*2.0001)/.0001=60003

As x approaches 2 from the right, f(x) approaches infinity.

Evaluate f(x) as x approaches 2 from the left:

f(1.9)=5.7/.1=57

f(1.99)=5.97/.01=597

f(1.999)=5.997/.001=5997

f(1.9999)=5.9997/.0001=59997

As x approaches 2 from the left, f(x) approaches negative infinity.

The limit as x approaches 2 from the left and the limit as x approaches 2 from the right do not converge and therefore the limit is undefined.

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