3 marksDifferentiation I
CAPE Pure Mathematics Unit 1 · May/June 2008 · Paper 2 · Question 6(a)(i)
Differentiate with respect to x: x√(2x - 1).
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- 6(a)(ii)Differentiate with respect to x: sin²(x³ + 4).[4 marks]
- 6(b)(i)Given that ∫(from 1 to 6) f(x) dx = 7, evaluate ∫(from 1 to 6) [2 - f(x)] dx.[3 marks]
- 6(b)(ii)Find the value of the constant k.[4 marks]
- 6(c)(i)a)Show that h = 45/r² - 2r/3.[3 marks]
- 6(c)(i)b)Show that A = 5πr²/3 + 90π/r, where A units is the external surface area of the can.[3 marks]
- 6(c)(ii)Hence, find the value of r for which A is a minimum and the corresponding minimum value of A.[5 marks]
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