1. Find dy/dx: 5x² 10X (a) y = 3√x - 5x² 3x (d) y = xe³x - ln(x² + 1)

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.2: Integration By Parts
Problem 34E
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Can you explain 1d's answer?

1. Find dy/dx:
11/2
3x¹²/2² -5x²
- 10x
X
(a) y = 3√x - 5x²
(d) y = xe ³a - In(x² + 1)
3x
2. Find the integrals, indefinite or definite:
1
(a) [ (2² - 2
-
X
(d)
(b) y =
2x + 5
(c) y = tan² (x)
x - 7
(e) 4x³ + y³ = 9y (in terms of x and y)
[²
(b) /
+ 2√x) dx
3x-2 dx
dx
[c²²-2 da (c) √√12 d
(x − 2)(x − 1) dx
-
(e) ["
0
¹/4 sin(2πx) dx
3. A wire 100 cm long is bent into the shape of a rectangle. A
child squeezes the top and bottom so that the rectangle be-
comes wider and shorter while its perimeter remains 100 cm.
How fast is the area of the rectangle decreasing when the
height is 20 cm and decreasing at 4 cm/sec? Include the
units.
5. A poster is to be made with a 1-inch margin on each of the left.
1
↓
个
4. A radioactive element decays to 80% of its original amount after 2 days. What is the
of this element? (An exact answer is preferred but not required.)
↓
个
1.5'
Transcribed Image Text:1. Find dy/dx: 11/2 3x¹²/2² -5x² - 10x X (a) y = 3√x - 5x² (d) y = xe ³a - In(x² + 1) 3x 2. Find the integrals, indefinite or definite: 1 (a) [ (2² - 2 - X (d) (b) y = 2x + 5 (c) y = tan² (x) x - 7 (e) 4x³ + y³ = 9y (in terms of x and y) [² (b) / + 2√x) dx 3x-2 dx dx [c²²-2 da (c) √√12 d (x − 2)(x − 1) dx - (e) [" 0 ¹/4 sin(2πx) dx 3. A wire 100 cm long is bent into the shape of a rectangle. A child squeezes the top and bottom so that the rectangle be- comes wider and shorter while its perimeter remains 100 cm. How fast is the area of the rectangle decreasing when the height is 20 cm and decreasing at 4 cm/sec? Include the units. 5. A poster is to be made with a 1-inch margin on each of the left. 1 ↓ 个 4. A radioactive element decays to 80% of its original amount after 2 days. What is the of this element? (An exact answer is preferred but not required.) ↓ 个 1.5'
1. Find dy/dx:
11/2
3x¹²/2² -5x²
- 10x
X
(a) y = 3√x - 5x²
(d) y = xe ³a - In(x² + 1)
3x
2. Find the integrals, indefinite or definite:
1
(a) [ (2² - 2
-
X
(d)
(b) y =
2x + 5
(c) y = tan² (x)
x - 7
(e) 4x³ + y³ = 9y (in terms of x and y)
[²
(b) /
+ 2√x) dx
3x-2 dx
dx
[c²²-2 da (c) √√12 d
(x − 2)(x − 1) dx
-
(e) ["
0
¹/4 sin(2πx) dx
3. A wire 100 cm long is bent into the shape of a rectangle. A
child squeezes the top and bottom so that the rectangle be-
comes wider and shorter while its perimeter remains 100 cm.
How fast is the area of the rectangle decreasing when the
height is 20 cm and decreasing at 4 cm/sec? Include the
units.
5. A poster is to be made with a 1-inch margin on each of the left.
1
↓
个
4. A radioactive element decays to 80% of its original amount after 2 days. What is the
of this element? (An exact answer is preferred but not required.)
↓
个
1.5'
Transcribed Image Text:1. Find dy/dx: 11/2 3x¹²/2² -5x² - 10x X (a) y = 3√x - 5x² (d) y = xe ³a - In(x² + 1) 3x 2. Find the integrals, indefinite or definite: 1 (a) [ (2² - 2 - X (d) (b) y = 2x + 5 (c) y = tan² (x) x - 7 (e) 4x³ + y³ = 9y (in terms of x and y) [² (b) / + 2√x) dx 3x-2 dx dx [c²²-2 da (c) √√12 d (x − 2)(x − 1) dx - (e) [" 0 ¹/4 sin(2πx) dx 3. A wire 100 cm long is bent into the shape of a rectangle. A child squeezes the top and bottom so that the rectangle be- comes wider and shorter while its perimeter remains 100 cm. How fast is the area of the rectangle decreasing when the height is 20 cm and decreasing at 4 cm/sec? Include the units. 5. A poster is to be made with a 1-inch margin on each of the left. 1 ↓ 个 4. A radioactive element decays to 80% of its original amount after 2 days. What is the of this element? (An exact answer is preferred but not required.) ↓ 个 1.5'
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