Rate Of Change Of Quantities | Ch 05 | Application Of Differentiation 02 Notes ; Polytechnic
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Hey Everyone, How are you ... Today I will show you How to Find rate Of Change of Quantities With respect to parameter chapter 05 , Application Of Differentiation ( Derivatives ), Which Is Module 02 Of Applied mathematics 02 .
Solution :
Rate Of Change Of Quantities | Ch 05 | Application Of Differentiation 02 Notes ; Polytechnic
Hey Everyone, How are you ... Today I will show you How to Find rate Of Change of Quantities With respect to parameter chapter 05 , Application Of Differentiation ( Derivatives ), Which Is Module 02 Of Applied mathematics 02 .
- Lecture 02 ( Topics ) :
1 ) Rate Of change Of Quantities - Basic Concept .
2 ) Some Important Questions .
3 ) Lecture Related Questions.
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| ( Overview Of Lecture ) |
1 ) Rate Of change Of Quantities - Basic Concept .
- Let Be a Quantity ( Area ) = Ï€ r²
Rate Of Change Of Area = dA/dR
= Change In Area / Change In radius
= Change In area per unit Change in radius
dA/dr = d ( Ï€r² ) / dr = 2Ï€r
*Notes :- Any Quantity Which is Change w.r.t to parameter .
= dQ / dp where, p = parameter
- Any Quantity Can Change in two ways.
1) Quantity Change W.r.t parameter
= dQ / dp
2) Quantity Change w.r.t time
= dQ / dt = dQ / dp × dp / dt
* Notes :-
( 1 ) Change in parameter increase w.r.t time = + Ve
( 2 )Change In Parameter decrease w.r.t time = -Ve
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| ( Basic Concept ) |
2 ) Some Important Questions
Question 01 )
Find The Rate of change of area of a circle w.r.t to its radius ( r ) , when r = 5 cm
Solution : View On This Page
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| ( Question 01 ) |
Question 02 )
Radius Of A Circle Increase @3cm/s .Find rate at which the area of the circle increasing when radius is 10 cm
Solution : View On This Page
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| ( Question 02 ) |
Question 03 )
The Length x of a rectangle is decreasing at the rate of 3 cm/min & width y is increasing at the rate of 2cm/min, when x = 10cm & y = 6cm , Find rate If Change of
( a ) Perimeter
( b ) Area
Solution : View On This Page
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| ( Question 03 ) |
Question 04 )
A particle Moves along the curve 6y = x³ + 2 ,Find the points On The curve at which y - Coordinate is Changing 8 times as fast as x coordinate.
Solution : View On This Page
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| ( Question 04 ) |
Question 05 )
A Man 2m high, walk at a uniform speed of 6 m per minute away form a lamp post, 5 m high . find the rate at which the length of his shadow increases.
Solution : View On This Page
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| ( Question 05 ) |
- Lecture Related Questions ;
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