14. Determine the constraints a and b such that f(x) is continuous for all values of x. [6 Marks] ax-b x ≤1 f(x) = x-21 -3x, 1
14. Determine the constraints a and b such that f(x) is continuous for all values of x. [6 Marks] ax-b x ≤1 f(x) = x-21 -3x, 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![14. Determine the constraints a and b such that f(x) is continuous for all values of x. [6 Marks]
ax-b
x ≤1
f(x) =
x-21
-3x,
1<x<2
bx²-a,
X ≥2
Section 4: Application
15. Solve the following limits (if possible): [3 Marks Each]
a) limx05+x
x
1
5
x3-27
b) lim x-3x²
-
9](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf41df8f-e300-4854-aaa2-c9c3c769a22c%2F758fa4d7-2e87-4f0f-a3a7-fd835d23a69e%2Fuiqk5aj_processed.png&w=3840&q=75)
Transcribed Image Text:14. Determine the constraints a and b such that f(x) is continuous for all values of x. [6 Marks]
ax-b
x ≤1
f(x) =
x-21
-3x,
1<x<2
bx²-a,
X ≥2
Section 4: Application
15. Solve the following limits (if possible): [3 Marks Each]
a) limx05+x
x
1
5
x3-27
b) lim x-3x²
-
9
![16. Using the limit as h goes to 0, find the slope of each of the following: [4 Marks, 5 Marks]
a) f(x)=-6x2 +7x-3 at x=-2
b) f(x)
x-8
=
at x = 1
2x+5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf41df8f-e300-4854-aaa2-c9c3c769a22c%2F758fa4d7-2e87-4f0f-a3a7-fd835d23a69e%2Fanrcgqk_processed.png&w=3840&q=75)
Transcribed Image Text:16. Using the limit as h goes to 0, find the slope of each of the following: [4 Marks, 5 Marks]
a) f(x)=-6x2 +7x-3 at x=-2
b) f(x)
x-8
=
at x = 1
2x+5
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