12X1 T04 01 rates of change (2011)
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Transcript of 12X1 T04 01 rates of change (2011)
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Rates of Change
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Rates of ChangeIn some cases two, or more, rates must be found to get the equation in terms of the given variable.
![Page 3: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/3.jpg)
Rates of Change
dtdx
dxdy
dtdy
In some cases two, or more, rates must be found to get the equation in terms of the given variable.
![Page 4: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/4.jpg)
Rates of Change
dtdx
dxdy
dtdy
In some cases two, or more, rates must be found to get the equation in terms of the given variable.
e.g. (i) A spherical balloon is being deflated so that the radius decreases at a constant rate of 10 mm/s.Calculate the rate of change of volume when the radius of the balloon is 100 mm.
![Page 5: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/5.jpg)
Rates of Change
dtdx
dxdy
dtdy
In some cases two, or more, rates must be found to get the equation in terms of the given variable.
?dtdV
e.g. (i) A spherical balloon is being deflated so that the radius decreases at a constant rate of 10 mm/s.Calculate the rate of change of volume when the radius of the balloon is 100 mm.
![Page 6: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/6.jpg)
Rates of Change
dtdx
dxdy
dtdy
In some cases two, or more, rates must be found to get the equation in terms of the given variable.
?dtdV
10dtdr
e.g. (i) A spherical balloon is being deflated so that the radius decreases at a constant rate of 10 mm/s.Calculate the rate of change of volume when the radius of the balloon is 100 mm.
![Page 7: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/7.jpg)
Rates of Change
dtdx
dxdy
dtdy
In some cases two, or more, rates must be found to get the equation in terms of the given variable.
?dtdV
10dtdr
e.g. (i) A spherical balloon is being deflated so that the radius decreases at a constant rate of 10 mm/s.Calculate the rate of change of volume when the radius of the balloon is 100 mm.
drdV
dtdr
dtdV
![Page 8: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/8.jpg)
Rates of Change
dtdx
dxdy
dtdy
In some cases two, or more, rates must be found to get the equation in terms of the given variable.
?dtdV
10dtdr
e.g. (i) A spherical balloon is being deflated so that the radius decreases at a constant rate of 10 mm/s.Calculate the rate of change of volume when the radius of the balloon is 100 mm.
2
3
4
34
rdrdV
rV
drdV
dtdr
dtdV
![Page 9: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/9.jpg)
Rates of Change
dtdx
dxdy
dtdy
In some cases two, or more, rates must be found to get the equation in terms of the given variable.
?dtdV
10dtdr
e.g. (i) A spherical balloon is being deflated so that the radius decreases at a constant rate of 10 mm/s.Calculate the rate of change of volume when the radius of the balloon is 100 mm.
2
3
4
34
rdrdV
rV
drdV
dtdr
dtdV
2
2
40410r
r
![Page 10: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/10.jpg)
Rates of Change
dtdx
dxdy
dtdy
In some cases two, or more, rates must be found to get the equation in terms of the given variable.
?dtdV
10dtdr
e.g. (i) A spherical balloon is being deflated so that the radius decreases at a constant rate of 10 mm/s.Calculate the rate of change of volume when the radius of the balloon is 100 mm.
2
3
4
34
rdrdV
rV
drdV
dtdr
dtdV
2
2
40410r
r
400000
10040,100when 2
dtdVr
![Page 11: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/11.jpg)
Rates of Change
dtdx
dxdy
dtdy
In some cases two, or more, rates must be found to get the equation in terms of the given variable.
?dtdV
10dtdr
e.g. (i) A spherical balloon is being deflated so that the radius decreases at a constant rate of 10 mm/s.Calculate the rate of change of volume when the radius of the balloon is 100 mm.
2
3
4
34
rdrdV
rV
drdV
dtdr
dtdV
2
2
40410r
r
400000
10040,100when 2
dtdVr
s/mm400000 of rate aat decreasingisvolumethemm,001isradiuswhen the
3
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(ii) A spherical bubble is expanding so that its volume increases at a constant rate of What is the rate of increase of its surface area when the radius is 10 mm?
/smm70 3
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(ii) A spherical bubble is expanding so that its volume increases at a constant rate of What is the rate of increase of its surface area when the radius is 10 mm?
/smm70 3
?dtdS
![Page 14: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/14.jpg)
(ii) A spherical bubble is expanding so that its volume increases at a constant rate of What is the rate of increase of its surface area when the radius is 10 mm?
/smm70 3
?dtdS 70
dtdV
![Page 15: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/15.jpg)
(ii) A spherical bubble is expanding so that its volume increases at a constant rate of What is the rate of increase of its surface area when the radius is 10 mm?
/smm70 3
?dtdS 70
dtdV
dS dV dS drdt dt dr dV
![Page 16: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/16.jpg)
(ii) A spherical bubble is expanding so that its volume increases at a constant rate of What is the rate of increase of its surface area when the radius is 10 mm?
/smm70 3
?dtdS 70
dtdV
2
3
4
34
rdrdV
rV
dS dV dS drdt dt dr dV
![Page 17: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/17.jpg)
(ii) A spherical bubble is expanding so that its volume increases at a constant rate of What is the rate of increase of its surface area when the radius is 10 mm?
/smm70 3
?dtdS 70
dtdV
2
3
4
34
rdrdV
rV
rdrdS
rS
8
4 2
dS dV dS drdt dt dr dV
![Page 18: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/18.jpg)
(ii) A spherical bubble is expanding so that its volume increases at a constant rate of What is the rate of increase of its surface area when the radius is 10 mm?
/smm70 3
?dtdS 70
dtdV
2
3
4
34
rdrdV
rV
rdrdS
rS
8
4 2
dS dV dS drdt dt dr dV
2
170 84
140
rr
r
![Page 19: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/19.jpg)
(ii) A spherical bubble is expanding so that its volume increases at a constant rate of What is the rate of increase of its surface area when the radius is 10 mm?
/smm70 3
?dtdS 70
dtdV
2
3
4
34
rdrdV
rV
rdrdS
rS
8
4 2
14 10
140,10when
dtdVr
dS dV dS drdt dt dr dV
2
170 84
140
rr
r
![Page 20: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/20.jpg)
(ii) A spherical bubble is expanding so that its volume increases at a constant rate of What is the rate of increase of its surface area when the radius is 10 mm?
/smm70 3
?dtdS 70
dtdV
2
3
4
34
rdrdV
rV
rdrdS
rS
8
4 2
14 10
140,10when
dtdVr
s/14mm of rate aat increasing isareasurfacethe10mmisradiuswhen
2
dS dV dS drdt dt dr dV
2
170 84
140
rr
r
![Page 21: 12X1 T04 01 rates of change (2011)](https://reader035.fdocuments.in/reader035/viewer/2022081404/55982ee91a28ab48178b46ed/html5/thumbnails/21.jpg)
Exercise 7E; 2, 5, 6, 9, 13*
Exercise 7F; 2, 5, 9, 10, 11*