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

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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)   (Show Source): You can put this solution on YOUR website!

a) lim x→3  

Factor

   lim x→3 

Cancel

   lim x→3 

Simplify and substitute:

   lim x→3 


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


b) lim x→∞ 

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

   lim x→∞ 

Simplify

   lim x→∞ 

Now use the fact that lim x→∞  = 0 on all the terms
except 15:

    

   lim x→∞ 

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

c) lim x→2 

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 

   lim x→2 

   lim x→2 

   lim x→2 

Edwin
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