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Finding rate of change
Ex 6.1, 1
Ex 6.1,17 (MCQ)
Example 5
Ex 6.1,15 Important
Example 6
Ex 6.1,16
Ex 6.1, 18 (MCQ) Important
Example 2
Ex 6.1,2
Example 35 You are here
Example 3
Ex 6.1,5 Important
Ex 6.1,3
Ex 6.1,6
Ex 6.1,12
Ex 6.1,13 Important
Misc 16 (MCQ)
Ex 6.1,14
Example 31 Important
Ex 6.1,4 Important
Example 30 Important
Example 4 Important
Ex 6.1,7
Ex 6.1,8
Ex 6.1,9
Ex 6.1,11 Important
Misc 2 Important
Ex 6.1,10 Important
Example 32 Important
Finding rate of change
Last updated at May 29, 2023 by Teachoo
Checking sign for numerator cos π₯ β sin π₯ > 0 cos π₯ > sin π₯ 1 > sinβ‘π₯/cosβ‘π₯ 1 > tan π₯ πππ§β‘π<π This is possible only if π<π<π /π Thus, fβ(π) = ((+))/((+) ) > 0 in x β (0 , π/4) Hence, f is strictly increasing function in (π , π /π) Let r be the radius of circle . & A be the Area of circle. Given that Radius increases at the rate of 0.05 cm/s Thus, π π/π π = 0.05 cm /sec We need to find rate of change of area of circle w. r. t time when r = 3.2 cm i.e. we need to find π π¨/π π when r = 3.2 cm We know that Area of circle = Οr2 A = Οr2 Differentiating w.r.t time π π¨/π π = π (π ππ)/π π ππ΄/ππ‘ = Ο π(π2)/ππ‘ ππ΄/ππ‘ = Ο π(π2)/ππ‘ Γ π π/π π ππ΄/ππ‘ = Ο π (ππ)/π π Γ ππ/ππ‘ ππ΄/ππ‘ = Ο. 2r . ππ/ππ‘ ππ΄/ππ‘ = 2Οr . π π/π π ππ΄/ππ‘ = 2Οr . 0.05 ππ΄/ππ‘ = 0.1 Γ Οr When π = 3.2 cm β ππ΄/ππ‘β€|_(π =10) = 0.1 Γ Ο Γ 3.2 β ππ΄/ππ‘β€|_(π =10) = 0.320Ο Since area is in cm2 & time is in seconds π π¨/π π = 0.320Ο cm2/s Hence, Area is increasing at the rate of 0.320Ο cm2/s when r = 0.32 cm