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Q7 of 29 Page 1

Differentiate tan–1


Using formula:

1 + cosx = 2 cos2(x/2) and


Now, we have,


[As we know that tanθ = cot (π/2 - θ)]



Now differentiating both sides we have,

()


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5

Prove that : 3 sin–1x = sin–1 (3x – 4x3), x ∈ .

6

Given A = compute A–1 and show that 2 A–1 = 9I – A.

8

The total cost C(x) associated with the production of x units of an item is given by C(x) = 0.005x3 – 0.02x2 + 30x + 5000. Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

9

Evaluate .

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