3. Find the values of a and b such that the following function is continuous at x = 4. Justify your answer. bx? -Зах -9 х <4 f(x) = { 56 + a x = 4 бах — 13 x > 4 (a) Find f(4) 4. Find the values of a and b such that the following function is continuous everywhere. Justify your answer. (a) ax? + 2bx - 19 x < 2 f(x) = {9 x = 2 4bx 15 x > 2 5. Use the Intermediate Value Theorem (IVT) to show that the equation below has a root in the associated interval. (a) 2x + x2 + x+3 = 0 (-2,0)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
3. Find the values of a and b such that the following function is continuous at x =
4. Justify
your answer.
bax? — Зах - 9
x < 4
|
f(x) = { 56 + a
x = 4
бах — 13
x > 4
(a) Find f(4)
4. Find the values of a and b such that the following function is continuous everywhere.
Justify your answer.
(a)
ax² + 2bx
19
x < 2
-
f(x) =
9.
x = 2
4bx – 15
x > 2
5. Use the Intermediate Value Theorem (IVT) to show that the equation below has a root
in the associated interval.
(a)
3
2x + x + x + 3 = 0
(-2,0)
Transcribed Image Text:3. Find the values of a and b such that the following function is continuous at x = 4. Justify your answer. bax? — Зах - 9 x < 4 | f(x) = { 56 + a x = 4 бах — 13 x > 4 (a) Find f(4) 4. Find the values of a and b such that the following function is continuous everywhere. Justify your answer. (a) ax² + 2bx 19 x < 2 - f(x) = 9. x = 2 4bx – 15 x > 2 5. Use the Intermediate Value Theorem (IVT) to show that the equation below has a root in the associated interval. (a) 3 2x + x + x + 3 = 0 (-2,0)
Instructions
42. The device shown below is the Atwood's machine considered in Example 6.5.
Assuming that the masses of the string and the frictionless pulley are negligible, (a)
find an equation for the acceleration of the two blocks; (b) find an equation for the
tension in the string; and (c) find both the acceleration and tension when block 1 has
mass 2.00 kg and block 2 has mass 4.00 kg.
Transcribed Image Text:Instructions 42. The device shown below is the Atwood's machine considered in Example 6.5. Assuming that the masses of the string and the frictionless pulley are negligible, (a) find an equation for the acceleration of the two blocks; (b) find an equation for the tension in the string; and (c) find both the acceleration and tension when block 1 has mass 2.00 kg and block 2 has mass 4.00 kg.
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