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Chapter 14: Q. 32 (page 883)

In Problems 7鈥� 42, find each limit algebraically.

limx鈫�-3x2+x-6x2+2x-3.

Short Answer

Expert verified

The answer is54.

Step by step solution

01

Step. 1 Given Information

Firstly, we check whether the given function is in indeterminant form or not.

f(x)=x2+x-6x2+2x-3

Put x=-3in numerator we get,

x2+x-6=(-3)2+(-3)-6=9-3-6=9-9=0.

Put x=-3in denominator we get,

x2+2x-3=(-3)2+2(-3)-3=9-6-3=9-9=0.

Since both numerator and denominator gives 0 means they both have x=-3as their common root.

02

Step. 2 Factorizing

Numerator, x2+x-6=(x+3)(x-2).

Denominator, x2+2x-3=(x+3)(x-1).

So,

limx鈫�-3x2+x-6x2+2x-3=limx鈫�-3(x+3)(x-2)(x+3)(x-1)=limx鈫�-3x-2x-1.

Now we can put the limit directly.

03

Step. 3 Final calculation of the limit 

limx鈫�-3x-2x-1=-3-2-3-1=-5-4=54.

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