If f(x) is continuous false 2. Assume that f(t) is continuous on [1,5] and that f(1) = 20, f(5) = 100. Determine statements is always true, never true, or sometimes true. (a) f(c) = 3 has a solution with c € [1, 5]. Never Truz Sometimes true (b) f(c) = 75 has a solution with c E [1,5]. Always true (e) f(c) = 50 has no solution with c E [1, 5]. Never true (d) f(c) = 30 has exactly one solution with c E [1,5]. Sometimes true 3. Use the IVT to show that f(x) = x³ + x takes on the value 9 for some x in [1, 2]. 4. Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that f(x) = x - cosa ha 5. Use the IVT to find an interval of length containing a root of f(x) = x³ + 2x +1. 6. Prove using the IVT. (i) √c+√c+2=3 has a solution. (ii) 2 = bx has a solution if b> 2. (iii) 2 + 3 = 4* has a solution. (iv) tan x= x has infinitely many solutions. 7. Find an interval of length in [1, 2] containing a root of the equation x7 + 3x - 10 = 0 Holy Cross 8. Evaluate lim 818 9. Evaluate lim H-X sin x I x² + x 3-x 10. Evaluate lim x²-x 818 12. Evaluate lim 11. Evaluate lim √x²+x-x H48 1+3x x+∞ √√2x²+x
If f(x) is continuous false 2. Assume that f(t) is continuous on [1,5] and that f(1) = 20, f(5) = 100. Determine statements is always true, never true, or sometimes true. (a) f(c) = 3 has a solution with c € [1, 5]. Never Truz Sometimes true (b) f(c) = 75 has a solution with c E [1,5]. Always true (e) f(c) = 50 has no solution with c E [1, 5]. Never true (d) f(c) = 30 has exactly one solution with c E [1,5]. Sometimes true 3. Use the IVT to show that f(x) = x³ + x takes on the value 9 for some x in [1, 2]. 4. Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that f(x) = x - cosa ha 5. Use the IVT to find an interval of length containing a root of f(x) = x³ + 2x +1. 6. Prove using the IVT. (i) √c+√c+2=3 has a solution. (ii) 2 = bx has a solution if b> 2. (iii) 2 + 3 = 4* has a solution. (iv) tan x= x has infinitely many solutions. 7. Find an interval of length in [1, 2] containing a root of the equation x7 + 3x - 10 = 0 Holy Cross 8. Evaluate lim 818 9. Evaluate lim H-X sin x I x² + x 3-x 10. Evaluate lim x²-x 818 12. Evaluate lim 11. Evaluate lim √x²+x-x H48 1+3x x+∞ √√2x²+x
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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![false
If f(x) is contin
2. Assume that f(t) is continuous on [1,5] and that f(1) = 20, f(5)= 100. Det
statements is always true, never true, or sometimes true.
(a) f(c) = 3 has a solution with ce [1,5]. Never True Sometimes true
(b) f(c) = 75 has a solution with c € [1,5]. Alway true
(e) f(c) = 50 has no solution with c E [1,5]. Never true
(d) f(c) = 30 has exactly one solution with c E [1, 5]. Sometimes true
3. Use the IVT to show that f(x) = x³ + x takes on the value 9 for some x in [1, 2].
4. Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that f(x) = x - cos has a
5. Use the IVT to find an interval of length
containing a root of f(x) = x³ + 2x +1.
6. Prove using the IVT.
(i) √c+√c+2=3 has a solution.
(ii) 2 = bx has a solution if b > 2.
(iii) 2 + 3 = 4 has a solution.
(iv) tan x= x has infinitely many solutions.
7. Find an interval of length 1
sin x
8. Evaluate lim
848
9. Evaluate lim
81X
I
x² + x
3 x
10. Evaluate lim x²-x
H4X
12. Evaluate lim
11. Evaluate lim √x²+x-x
H48
1+3x
x+∞ √√2x²+x
in [1, 2] containing a root of the equation 7 + 3x - 10 = 0.
Holy
Cross](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96c43769-2331-4d91-b7f9-4a256a33e785%2F9c0df7eb-233a-4455-a5fc-722a541889b0%2Fh5ycj92_processed.jpeg&w=3840&q=75)
Transcribed Image Text:false
If f(x) is contin
2. Assume that f(t) is continuous on [1,5] and that f(1) = 20, f(5)= 100. Det
statements is always true, never true, or sometimes true.
(a) f(c) = 3 has a solution with ce [1,5]. Never True Sometimes true
(b) f(c) = 75 has a solution with c € [1,5]. Alway true
(e) f(c) = 50 has no solution with c E [1,5]. Never true
(d) f(c) = 30 has exactly one solution with c E [1, 5]. Sometimes true
3. Use the IVT to show that f(x) = x³ + x takes on the value 9 for some x in [1, 2].
4. Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that f(x) = x - cos has a
5. Use the IVT to find an interval of length
containing a root of f(x) = x³ + 2x +1.
6. Prove using the IVT.
(i) √c+√c+2=3 has a solution.
(ii) 2 = bx has a solution if b > 2.
(iii) 2 + 3 = 4 has a solution.
(iv) tan x= x has infinitely many solutions.
7. Find an interval of length 1
sin x
8. Evaluate lim
848
9. Evaluate lim
81X
I
x² + x
3 x
10. Evaluate lim x²-x
H4X
12. Evaluate lim
11. Evaluate lim √x²+x-x
H48
1+3x
x+∞ √√2x²+x
in [1, 2] containing a root of the equation 7 + 3x - 10 = 0.
Holy
Cross
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