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3. Consider this function: 4.x + a if x < 3 f (x) = 3x2 – 7x – 2a if x > 3 - 23 – 46 if x = 3. Suppose I tell you that f(x) is continuous at x = 3. Find a and b.

3. Consider this function: 4.x + a if x < 3 f (x) = 3x2 – 7x – 2a if x > 3 - 23 – 46 if x = 3. Suppose I tell you that f(x) is continuous at x = 3. Find a and b.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Consider this function: 4.x + a if x < 3 f (x) = { 3.x2 – 7.x – 2a if x > 3 23 – 46 if x = 3. Suppose I tell you that f(x) is continuous at x = 3. Find a and b.
Transcribed Image Text:3. Consider this function: 4.x + a if x < 3 f (x) = { 3.x2 – 7.x – 2a if x > 3 23 – 46 if x = 3. Suppose I tell you that f(x) is continuous at x = 3. Find a and b.
Expert Solution
Step 1

the function is continuous at x=3

therefore, limx→3-fx=limx→3+fx=f3

now 

limx→3-fx=limx→3-x2-4x+a=32-43+a=9-12+a=-3+a

Step 2

limx→3+fx=limx→3+3x2-7x-2a=332-73-2a=27-21-2a=6-2a

limx→3-fx=limx→3+fx-3+a=6-2a-3-6=-2a-a-9=-3a-9-3=a3=a

therefore value of a = 3

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