Remainders and estimates Consider the following convergent series. a. Find an upper bound for the remainder in terms of n. b. Find how many terms are needed to ensure that the remainder is less than 10 −3 . c. Find lower and upper bounds (L n and U n , respectively) on the exact value of the series. d. Find an interval in which the value of the series must lie if you approximate it using ten terms of the series. 35. ∑ k = 1 ∞ 1 k 6
Remainders and estimates Consider the following convergent series. a. Find an upper bound for the remainder in terms of n. b. Find how many terms are needed to ensure that the remainder is less than 10 −3 . c. Find lower and upper bounds (L n and U n , respectively) on the exact value of the series. d. Find an interval in which the value of the series must lie if you approximate it using ten terms of the series. 35. ∑ k = 1 ∞ 1 k 6
Is the function f(x) continuous at x = 1?
(z)
6
5
4
3.
2
1
0
-10
-9
-7
-5
-2
-1 0
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
Select the correct answer below:
○ The function f(x) is continuous at x = 1.
○ The right limit does not equal the left limit. Therefore, the function is not continuous.
○ The function f(x) is discontinuous at x = 1.
○ We cannot tell if the function is continuous or discontinuous.
Is the function f(x) shown in the graph below continuous at x = −5?
f(x)
7
6
5
4
2
1
0
-10
-9
-8 -7
-6
-5
-4
-3
-2
-1 0
1
2
3
4
5
6 7 8 9
10
-1
-2
-3
-4
-5
-6
-7
Select the correct answer below:
The function f(x) is continuous.
○ The right limit exists. Therefore, the function is continuous.
The left limit exists. Therefore, the function is continuous.
The function f(x) is discontinuous.
○ We cannot tell if the function is continuous or discontinuous.
4. Evaluate the following integrals. Show your work.
a)
-x
b) f₁²x²/2 + x² dx
c) fe³xdx
d) [2 cos(5x) dx
e) √
35x6
3+5x7
dx
3
g) reve
√ dt
h) fx (x-5) 10 dx
dt
1+12
Chapter 10 Solutions
Calculus: Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)
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