math

thanks for the explanation of limit, but i want someone to help check out this problem for me

lim x->3 (x^2 - x - 12)/ (x - 3)
i got 5 as the answer

okay, so i cant use substitution.

i factor the (x^2 - x - 12) and got (x - 4) and (x + 3)

[(x - 4)(x + 3)]/ (x - 3)

i cant cancel anything out though
so i use multiply by the conjugate

[(x^2 - x - 12)/(x - 3)] [(x + 3) / (x + 3)] -->
(x^3 + 2x^2 - 15x -36) / (x^2 - 9)

then
numerator:
1/x^2 (x^3 + 2x^2 - 15x -36) -->
x + 2 - 15/x - 36/x^2

denominator:
1/x^2 (x^2 - 9) -->
1 - 9/x^2

got:
[x + 2 - 15/x - 36/x^2] over [1 - 9/x^2] -->
[x + 2 - 0 - 0] over [1 - 0] -->
3+ 2 = 5

is this right?


Are you sure you copied the problem correcty? It makes more sense if you are asked the limit of
(x^2 + x - 12)/ (x - 3),
For (x^2 - x - 12)/ (x - 3), as x>3 , the function becomes 6/0, which is infinity.


You should have gone no further than here:

[(x - 4)(x + 3)]/ (x - 3)

At this point you just examine the numerator and denominator. If the limit of the numerator is N and the limit of denominator is D, and if D is not zero, then the limit is:

N/D

If D is zero, like in this case, then there are two cases. Either N is non-zero, in which case the limit does not exist. Or N is also zero. In that case you need to investigate furher.

In this case N is nonzero, so the limit does not exist.

drwls - yes im sure i copied it right. i know it would have been much easier if it was (x^2 + x - 12). i don't know if this is a typo made by my instructor

Count Iblis - oh yea i forgot all about that rule. wow thanks a lot, wish i had realized it earlier to save tons of time

  1. 👍 0
  2. 👎 0
  3. 👁 145
asked by glen

Respond to this Question

First Name

Your Response

Similar Questions

  1. math-calculus

    1.For any function y+f(x), express dy/dx using limit notation. Give a clear explanation for your given answer. you probably meant to type y=f(x) By definition dy/dx = Limit (f(x+∆x) - f(x))/∆x as ∆x-->0 The explanation of

    asked by Chris on March 26, 2007
  2. math

    How to solve for delta using trig functions? i.e. cosine sine tangent secant Thank you I'm not sure what delta you're referring to. Could you please elaborate some for us. What is it you're trying to do with the trig funtions? the

    asked by Kali on September 6, 2006
  3. Calculus II

    Hello! I have a problem on volumes but I am having trouble visualizing the object. y=ln(x), y=1, y=2, x=0, about the y-axis For the graph, I graphed y=ln(x), then I have from 1 to 2. Is this one with a washer where I have integral

    asked by Shelley on February 10, 2007
  4. math

    the limit of cuberoot((-3x^3+5x+2)/(x^2-1)) as x approaches 3 is the problem. how could (-3x^3+5x+2) so it would be factored out with denominator? thanks! If you read the answer I gave for the previous question, then you can take

    asked by . on September 3, 2006
  5. Calculus

    Is this the right explanation for this question 1. Examine the continuity of the function h(x)= -x, if x0 Answer: Since h(x)= -x, if x0 is h=|x|, we can conclude that the function is 1. continuous everywhere 2. discontinuous at

    asked by Matthew on February 11, 2012
  1. math

    can someone please explain this problem? (-> is an arrow) assume that limit x-> 4 f(x)=0 and limit x-> 4 g(x)=3 1. limit x-> 4 (g(x)+3

    asked by alice on September 3, 2009
  2. Calculus

    I need some help on getting ideas for my limits & continuity calculus project! For the limits project: I have to conduct an "interview with a limit" (Q&A format).I have to include factual information like definitions, properties,

    asked by RJ on October 19, 2008
  3. Math- Ideas only

    I need some help on getting ideas for my limits & continuity calculus project! For the limits project: I have to conduct an "interview with a limit" (Q&A format).I have to include factual information like definitions, properties,

    asked by RJ on October 19, 2008
  4. Calculus

    1. Use the Taylor series to calculate the limit. Problem: limit as x approaches 0 is equal to (1-cos(x))/(1+x-e^x). I did the problem out but I need help in seeing if its correct. limit as x approaches 0 is equal to

    asked by Joshua on April 28, 2009
  5. calculus

    I'm not sure how to find the limit of this problem :S limit as x -> 0+ (cos(x))^(1/x^2)

    asked by James on May 31, 2010

More Similar Questions