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- Demonstrate an understanding the concept of differential and Integral Calculus;
- Demonstrate an understanding how to calculate and solve engineering problem using differential and Integral Calculus.
Question: 1 Differentiate the following with respect to the variable:
1) y = 5 cos2x+11 2) y = e0.5x-1 3) y = 4 ln t/2+104) y = ex/x2 5) y = 2√(x2-1) 6) y = 2x3- 4/x3 + 4√(x3 ) + 607) f(θ) = 2sin?(4θ+1) - cos?(3θ-1)
Question: 2 Locate the turning point on the curve y=3x2 - 6x + 1. And determine whether it is a maximum or minimum.
Question: 3 Determine:
1) ∫√x dx
2) ∫(1-x)2 dx
3) 4∫?x dx
4) 1∫2x2 dx
5) ∫ tanx.sec2x dx
Question: 4 Determine :
1) ∫(2x-1)8 dx
2) ∫ lnθ/θ dθ
Question: 5 Determine 4∫512/(x2-9) dx
Question: 6 Using the method of integration by parts, determine
1) ∫ x ex dx 2) 1∫2 lnx dx Question: 7 A spherical balloon is being blown up such that its volume increases at the constant rate of 2.00 m3/min. Find the rate (m/min) at which the radius is increasing when it is 1.00 m.
Question: 8 Show that ∫dx/(x2 + a2) = 1/a tan-1 x/a + C by using the substitution x = a tanθ.
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