SOLUTION: Hi all, I need to find out how find each of the following limits. I dont expect all the answers, but help on how to solve each woould be great. a) lim x→3 3x^2-7x-6 / 2x^2+x

Algebra ->  Graphs -> SOLUTION: Hi all, I need to find out how find each of the following limits. I dont expect all the answers, but help on how to solve each woould be great. a) lim x→3 3x^2-7x-6 / 2x^2+x      Log On


   

Question 205324: Hi all, I need to find out how find each of the following limits. I dont expect all the answers, but help on how to solve each woould be great.
a) lim x→3 3x^2-7x-6 / 2x^2+x-21
b) lim x→∞ 12x^4+5x+12 / 15x^5+14x-3
c) lim x→2 x-2 / sqrt(x+5) - sqrt(7)
Would really help me out.
Thanks, -Nick.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

a) lim x→3 %28%283x%5E2-7x-6%29+%2F+%282x%5E2%2Bx-21%29%29 

Factor

   lim x→3 %28%28%283x%2B2%29%28x-3%29%29+%2F+%282x%2B7%29%28x-3%29%29%29

Cancel

   lim x→3 %28%28%283x%2B2%29%28cross%28x-3%29%29%29+%2F+%282x%2B7%29%28cross%28x-3%29%29%29%29

Simplify and substitute:

   lim x→3 


=========================================


b) lim x→∞ %28%2812x%5E4%2B5x%2B12%29+%2F+%2815x%5E5%2B14x-3%29%29

It's different when x approaches infinity.  The
highest power of x that appears is x%5E5.
So divide every term by x%5E5

   lim x→∞ 

Simplify

   lim x→∞ %28%2812%2Fx%2B5%2Fx%5E4%2B12%2Fx%5E5%29+%2F+%2815%2B14%2Fx%5E4-3%2Fx%5E5%29%29

Now use the fact that lim x→∞ k%2Fx%5En = 0 on all the terms
except 15:

    %28%280%2B0%2B0%29+%2F+%2815%2B0-0%29%29=0%2F15=0

   lim x→∞ 

=================================================

c) lim x→2 %28%28x-2%29+%2F%28sqrt%28x%2B5%29+-+sqrt%287%29%29%29

Multiply by the conjugate of the denominator over itself:

   lim x→2 

Now FOIL out the bottom, leave the top as is:

   lim x→2 

   lim x→2 

   lim x→2 %28%28x-2%29%28sqrt%28x%2B5%29+%2B+sqrt%287%29%29%29%2F%28%28x%2B5%29-7%29

   lim x→2 %28%28x-2%29%28sqrt%28x%2B5%29+%2B+sqrt%287%29%29%29%2F%28%28x-2%29%29

   lim x→2 %28%28cross%28x-2%29%29%28sqrt%28x%2B5%29+%2B+sqrt%287%29%29%29%2F%28%28cross%28x-2%29%29%29

   lim x→2 

Edwin