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
100%
![18:44
MAT 32102: Limits & Cont.
that f is continuous on (-∞, ∞).
9. If f(x) = x² + 10 sinr show that there is a number c such that f(c) = 1000.
10. Prove that if f is a continuous function on an interval, then so is [x].
5+√√x
z+4√√5 + x
(a) lim
(a) z¹+z-3=0, (1, 2)
(b) √x=1-x, (0, 1)
(c) cos x = x, (0, 1)
(d) Inze, (1,2)
12. Use continuity to evaluate each limit.
(b) lim sin(x + sin x)
I-
11. Use the intermediate value theorem to show that there is a root of the given
equation in the specified interval.
(c) lim e²²-z
r1
(d) lim tan-1
MAT 321...ontinuity
Page 2
F. Chamera
(c) f(x) =
3x² - 6x
13. suppose f is continuous on [1, 5] and the only solutions of the equation f(x) = 6
are x = 1 and x = 4. If f(2)= 8, determine why f(3) > 6.
14. Prove that lim z cos = 0.
15. Prove that lim √resin(/) = 0.
I→0+
(a) f(x) = x² + √7-x, a = 4
(b) f(x) = (x + 2x³)4, a = -1
2x - 3x²
1+73, a=1
2x +3
(d) f(x) =
16. Suppose f and g are continuous functions such that g(2) = 6 and
lim[3f(x) + f(x)g(x)] = 36. Find f(2).
QOFill
17. Show that the function is continuous at the given number a or the given
interval.
(2,00)
x-2
(e) f(x) = 2√3x, (-0,3)
|||
August 2023
18. Prove that f is continuous at a if and only if lim f(a+h) = f(a).
h→0
Page 3
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Transcribed Image Text:18:44
MAT 32102: Limits & Cont.
that f is continuous on (-∞, ∞).
9. If f(x) = x² + 10 sinr show that there is a number c such that f(c) = 1000.
10. Prove that if f is a continuous function on an interval, then so is [x].
5+√√x
z+4√√5 + x
(a) lim
(a) z¹+z-3=0, (1, 2)
(b) √x=1-x, (0, 1)
(c) cos x = x, (0, 1)
(d) Inze, (1,2)
12. Use continuity to evaluate each limit.
(b) lim sin(x + sin x)
I-
11. Use the intermediate value theorem to show that there is a root of the given
equation in the specified interval.
(c) lim e²²-z
r1
(d) lim tan-1
MAT 321...ontinuity
Page 2
F. Chamera
(c) f(x) =
3x² - 6x
13. suppose f is continuous on [1, 5] and the only solutions of the equation f(x) = 6
are x = 1 and x = 4. If f(2)= 8, determine why f(3) > 6.
14. Prove that lim z cos = 0.
15. Prove that lim √resin(/) = 0.
I→0+
(a) f(x) = x² + √7-x, a = 4
(b) f(x) = (x + 2x³)4, a = -1
2x - 3x²
1+73, a=1
2x +3
(d) f(x) =
16. Suppose f and g are continuous functions such that g(2) = 6 and
lim[3f(x) + f(x)g(x)] = 36. Find f(2).
QOFill
17. Show that the function is continuous at the given number a or the given
interval.
(2,00)
x-2
(e) f(x) = 2√3x, (-0,3)
|||
August 2023
18. Prove that f is continuous at a if and only if lim f(a+h) = f(a).
h→0
Page 3
<
Transcribed Image Text:14:30
15:00
15:30
16:00
16:30 lim x²³ - B
x6-66
17:00 b
17:30
Evaluate
18:00 lim
18:30 O
19:00
19:30 11m
20:00 Yo
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8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31
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1-cosy
FEBRUARY 2023
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S M T W
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2 3 4
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5 6 7
9 10 11
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19 20 21 22 23 24 25
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