# Prove that

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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