
Concept explainers
Find the limit algebraically.

Answer to Problem 1CT
The limit of the function is −0.75
Explanation of Solution
Given information:
Sketch a graph of the function and approximate the limit (if it exists). Then find the limit (if it exists) algebraically by using appropriate technique(s).
limx→−2x2−12x
Calculation:
Consider the given function,
limx→−2x2−12x
Sketch a graph of the function use graphing utility TI−83
Press Y and key and observe the screen,
Now press WINDOW to choose proper scale,
Now press GRAPH and display will be,
Now verify the existence of limit, Press 2nd window and display will be.
Now enter the values of X as X=1.9,1.99,2,2.001,2.01,2.1 and ENTER successively.
As the value of the function approaches to the same value as X approaches from left and right the limit at x=−2 exists.
Now evaluate the limit of function by substitution x=−2 by direct substitute method.
limx→−2x2−12x=(−2)2−12(−2)=4−1−4=−34=−0.75
Hence the limit of the function is −0.75
Chapter 12 Solutions
EBK PRECALCULUS W/LIMITS
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