Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
Related questions
Question
only 14
![1-4 Find the value of
(a)
Σf(x) Axx
(b) max Axk.
k=1
1. f(x) = x + 1; a = 0,b= 4; n = 3;
Ax₁ = 1, Ax₂ = 1, Ax3 = 2;
x₁ = x₂ = x3 = 3
2. f(x) = cos x; a = 0, b = 2π; n = 4;
Ax₁ = π/2, Ax₂ = 3/4, Ax3 = π/2, Ax4 = π/4;
x₁ = π/4, x₂ = π, x3 = 3π/2₁x₁ = 7π/4
3. f(x) = 4x²; a = −3, b = 4; n = 4;
Ax₁ = 1, Ax2 = 2, Ax3 = 1, Ax4 = 3;
x₁ = -2, x₂ =
-1, x3* = 1,x4 = 3
4. f(x) = x³; a =
−3, b = 3; n = 4;
Ax₁ = 2, A.x2 = 1, Ax3 = 1, Ax4 = 2;
x₁ = -2, x₂ = 0, x3 =0, x=2
5-8 Use the given values of a and b to express the following
limits as integrals. (Do not evaluate the integrals.)
5.
lim
Σ(x)²Axx; a=-1, b = 2
max Δ.Χ. -1 0
k=1
6.
lim
[(x)³ Axk; a = 1, b = 2
max Ax → 04
k=1
7. lim
4x (1-3x)Axk; a = -3, b=3
8. lim
(sin²x)Axx; a = 0,b= π/2
max Ax → 0
9-10 Use Definition 5.5.1 to express the integrals as limits of
Riemann sums. (Do not evaluate the integrals.)
9. (a)
2x dx
(b)
• √ √ √ √ x ²
dx
+
• f₁²2x
1²
TT/2
10. (a)
√x dx
(b)
(1 + cos x) dx
-π/2
FOCUS ON CONCEPTS
11. Explain informally why Theorem 5.5.4(a) follows from
Definition 5.5.1.
12. Explain informally why Theorem 5.5.6(a) follows from
Definition 5.5.1.
13-16 Sketch the region whose signed area is represented by
the definite integral, and evaluate the integral using an appro-
priate formula from geometry, where needed.
13. (a)
T²²
x dx
(b)
[x
(c)
» [₁
x dx
1 L¸ x d
-5
max Ax0
k=1
(d)
x dx
14. (a)
(b)
[² (1-x) dx
[² (1 – ½x) dx
› [²₁ (1 - 1x) dx
(1-x) dx
(c)
(d)
15. (a)
2 dx
(b)
COS.
cos x dx
(c)
1₁
|2x - 3| dx
(d)
√1-x² dx
16. (a)
[
6 dx
(b)
sin x dx
(c)
S² |x2| dx
(d)
[²
√4x² dx
17. In each part, evaluate the integral, given that
Sx-2,
f(x) =
x>0
x < 0
1x + 2,
(a)
I fo
(b)
1500
f(x) dx
(c)
[ Fox
f(x) dx
(d) [ f(x) dx
18. In each part, evaluate the integral, given that
f(x) = { 2x
(2x, x≤1
x > 1
f(x) dx
(b)
(a) [
[ f(x) dx
[ f(x)
f₁fx
(c)
(d)
FOCUS ON CONCEPTS
19-20 Use the areas shown in the figure to find
(a)
fre
f(x) dx
(b)
›) [ f(x) dx
(d) ["f(x) dx.
(c)
[ f(x) dx
19.
AV
Area=0.8 Area = 1.5.
a b
Area = 2.6
f(x) dx
21. Find
22. Find
L
1²,50
5₁
y = f(x)
X
/c d
[f(x) + 2g(x)] dx if
f(x) dx = 5 and
[3f(x) = g(x)] dx if
*f(x) dx = 2 and
1₁
T/3
f(x) dx
f(x) dx
20.
AY Area = 10
TA
a b
Area 941
1₁86
[*8(x)
Area 9
y = f(x)
g(x) dx = -3
g(x) dx = 10
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa674ff5f-217c-4679-8de2-4438e48efc75%2F80130612-cfad-41ec-b567-e2bc2eace59a%2Fkg6t0ca_processed.png&w=3840&q=75)
Transcribed Image Text:1-4 Find the value of
(a)
Σf(x) Axx
(b) max Axk.
k=1
1. f(x) = x + 1; a = 0,b= 4; n = 3;
Ax₁ = 1, Ax₂ = 1, Ax3 = 2;
x₁ = x₂ = x3 = 3
2. f(x) = cos x; a = 0, b = 2π; n = 4;
Ax₁ = π/2, Ax₂ = 3/4, Ax3 = π/2, Ax4 = π/4;
x₁ = π/4, x₂ = π, x3 = 3π/2₁x₁ = 7π/4
3. f(x) = 4x²; a = −3, b = 4; n = 4;
Ax₁ = 1, Ax2 = 2, Ax3 = 1, Ax4 = 3;
x₁ = -2, x₂ =
-1, x3* = 1,x4 = 3
4. f(x) = x³; a =
−3, b = 3; n = 4;
Ax₁ = 2, A.x2 = 1, Ax3 = 1, Ax4 = 2;
x₁ = -2, x₂ = 0, x3 =0, x=2
5-8 Use the given values of a and b to express the following
limits as integrals. (Do not evaluate the integrals.)
5.
lim
Σ(x)²Axx; a=-1, b = 2
max Δ.Χ. -1 0
k=1
6.
lim
[(x)³ Axk; a = 1, b = 2
max Ax → 04
k=1
7. lim
4x (1-3x)Axk; a = -3, b=3
8. lim
(sin²x)Axx; a = 0,b= π/2
max Ax → 0
9-10 Use Definition 5.5.1 to express the integrals as limits of
Riemann sums. (Do not evaluate the integrals.)
9. (a)
2x dx
(b)
• √ √ √ √ x ²
dx
+
• f₁²2x
1²
TT/2
10. (a)
√x dx
(b)
(1 + cos x) dx
-π/2
FOCUS ON CONCEPTS
11. Explain informally why Theorem 5.5.4(a) follows from
Definition 5.5.1.
12. Explain informally why Theorem 5.5.6(a) follows from
Definition 5.5.1.
13-16 Sketch the region whose signed area is represented by
the definite integral, and evaluate the integral using an appro-
priate formula from geometry, where needed.
13. (a)
T²²
x dx
(b)
[x
(c)
» [₁
x dx
1 L¸ x d
-5
max Ax0
k=1
(d)
x dx
14. (a)
(b)
[² (1-x) dx
[² (1 – ½x) dx
› [²₁ (1 - 1x) dx
(1-x) dx
(c)
(d)
15. (a)
2 dx
(b)
COS.
cos x dx
(c)
1₁
|2x - 3| dx
(d)
√1-x² dx
16. (a)
[
6 dx
(b)
sin x dx
(c)
S² |x2| dx
(d)
[²
√4x² dx
17. In each part, evaluate the integral, given that
Sx-2,
f(x) =
x>0
x < 0
1x + 2,
(a)
I fo
(b)
1500
f(x) dx
(c)
[ Fox
f(x) dx
(d) [ f(x) dx
18. In each part, evaluate the integral, given that
f(x) = { 2x
(2x, x≤1
x > 1
f(x) dx
(b)
(a) [
[ f(x) dx
[ f(x)
f₁fx
(c)
(d)
FOCUS ON CONCEPTS
19-20 Use the areas shown in the figure to find
(a)
fre
f(x) dx
(b)
›) [ f(x) dx
(d) ["f(x) dx.
(c)
[ f(x) dx
19.
AV
Area=0.8 Area = 1.5.
a b
Area = 2.6
f(x) dx
21. Find
22. Find
L
1²,50
5₁
y = f(x)
X
/c d
[f(x) + 2g(x)] dx if
f(x) dx = 5 and
[3f(x) = g(x)] dx if
*f(x) dx = 2 and
1₁
T/3
f(x) dx
f(x) dx
20.
AY Area = 10
TA
a b
Area 941
1₁86
[*8(x)
Area 9
y = f(x)
g(x) dx = -3
g(x) dx = 10
X
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