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Chapter 14: Q. 8 (page 905)

limx鈫�-3x2-9x2-x-12find the limit

Short Answer

Expert verified

limx鈫�-3x2-9x2-x-12=67

Step by step solution

01

Step 1. Given information 

limx鈫�-3x2-9x2-x-12

02

Step 2. Domain of the function

We can find limit of rational function by limx鈫�cf(x)=f(c)if c is in the domain of f(x) .So to find the domain of f(x)=x2-9x2-x-12we have to put denominator =0

role="math" localid="1647084893764" x2-x-12x=-3x=4

So domain of the f(x) is all real number except 4and -3.

03

Step 3. limit of the function

As here c= -3which is not in the domain . So we have to simplify the f(x)

limx鈫�-3x2-9x2-x-12=limx鈫�-3(x-3)(x+3)(x-4)(x+3)=limx鈫�-3x-3x-4=-3-3-3-4=67


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