SOLUTION: 3. Let f(x) =x + 2p if x < −2, 3px + q if −2 ≤ x ≤ 1, 3x−2q if x > 1. Determine the values of p and q that make f continuous
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Question 1045663: 3. Let f(x) =x + 2p if x < −2, 3px + q if −2 ≤ x ≤ 1, 3x−2q if x > 1. Determine the values of p and q that make f continuous
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The limit of the function from the left of x = -2 should be equal to the limit of the function from the right of x = -2.
Upon substitution these give
-2 + 2p = 3p*-2+q <===> -2 + 2p = -6p + q <===> q = 8p - 2 <---Equation A
Similarly, The limit of the function from the left of x = 1 should be equal to the limit of the function from the right of x = 1.
Upon substitution these give
3p +q = 3-2q <===> 3p + 3q = 3 <===> p + q = 1 <---Equation B
After substituting Equation A into Equation B, we get
p + 8p - 2 = 1 ===> 9p = 3 ===> , and hence .
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