SOLUTION: For what value of the constants a and b such that the following limit exists: lim x→−1 (ax + |x + 1|)|x + b − 2|/ |x + 1| .

Question 1020220: For what value of the constants a and b such that the following limit exists:
lim
x→−1
(ax + |x + 1|)|x + b − 2|/
|x + 1|
.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!

Since the denominator approaches 0 as x goes to 0, the numerator also needs to go to zero.
If a = 0, then the numerator becomes
==> the quotient becomes after division by , hence any value of b will render the limit existent.
If , then the numerator approaches as x approaches -1, and the only possibility is for b = 3. The quotient then becomes
after division, and the limit of this expression exists as x -> -1 for whatever value of a.
Thus {a, b R|a = 0 and b is any real number} U { a,b R| b=3 and a is any real number} would render the limit above existent.
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SOLUTION: For what value of the constants a and b such that the following limit exists: lim x&#8594;&#8722;1 (ax + |x + 1|)|x + b &#8722; 2|/ |x + 1| .

SOLUTION: For what value of the constants a and b such that the following limit exists: lim x→−1 (ax + |x + 1|)|x + b − 2|/ |x + 1| .