SOLUTION: A2. Is there a number b such that {{{lim( x->-1, (2x^2+bx+3b)/(X^2-x-2))}}} exists? If so, fi nd the value of b and the value of the limit. Detail steps will be appreciated! Tha

Algebra ->  Testmodule -> SOLUTION: A2. Is there a number b such that {{{lim( x->-1, (2x^2+bx+3b)/(X^2-x-2))}}} exists? If so, fi nd the value of b and the value of the limit. Detail steps will be appreciated! Tha      Log On


   

Question 1036420: A2. Is there a number b such that
lim%28+x-%3E-1%2C+%282x%5E2%2Bbx%2B3b%29%2F%28X%5E2-x-2%29%29
exists? If so, fi nd the value of b and the value of the limit.
Detail steps will be appreciated! Thankyou
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
b = -1.

Can you complete the assignment with this hint?

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Comment from student: Hi, Sorry to bother! Do I just plugin the -1 into the b and simply the whole equation and I will able to find
the value of the limit? And how do I actually find b is equal to -1? Thank you!
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My response: 
1.  Yes, you can.
    plugin -1 into the "b" and simplify.
    Factor the resulting numerator, factor the denominator and cancel the common factors. 
    Then you will be able to find the limits.
    You are on the right track.

2.  How did I get this value of b?

    It is very simple. Factor the denominator: x%5E2-x-2 = (x+1)*(x-2).

    In order for this rational function would have the limit at x-> -1 (where the denominator becomes zero), 
    the numerator should be zero at x = -1.  Then the equation for the numerator 2x%5E2%2Bbx%2B3b = 0 at x = -1 gives this value for b.
    Otherwise the limit would be +/- infinity . . .

Your questions do not bother me.
They are reasonable, and I am glad to help.
Good luck!