Answer :

Given,



Key point: A function f(x) is said to be increasing over an interval [a, b] if f’(x) > 0 x [a, b]


To check whether y is increasing or not, we will differentiate it with respect to θ and will check its sign over the interval [0, π/2]




Applying the quotient rule of differentiation –





{ sin2θ + cos2θ = 1}





for θ [0, π/2] ; cos θ [0, 1]



Thus, we can say that y is increasing function in [0, π/2].


OR


Let, r = radius of sphere = 9 cm


Error in measurement = dr = 0.03


We know that the surface area of the sphere is given by 4πr2


Let A represents the area of the sphere.


A = 4πr2


Differentiating both sides w.r.t r –





{putting the values given in question}


dA = 2.16π cm2 = 6.786 cm2 {taking π = 3.1416}


Approximate error in surface area = 6.786 cm2


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