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Web Must vs Have to Exercise ( / Preintermediate) A multiplechoice exercise to practise modals of obligation must / mustn't, have to / don't have to Choose the

3 4 2 0 3 2 0 V 2πradius shellheightdx 2π(3 x)x dx 2π (3 x x) dx 5 56 5 28 0 2 5 32 2 12 4 5 3 2 2 0 5 π 4 π π = π − = = − = − x x We could also find this volume using the washer method First the function needs to be rewritten in terms of y x = f(y) = y1/3, 0 ≤ y ≤ 8 The washer has an outer radius of R = 3 − y1/3 (asAt any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (4, 3) Find the equation of the curve given that it passes through ( Facebook Whatsapp Transcript Ex 63, 11 Solve the following system of inequalities graphically 2x y ≥ 4, x y ≤ 3, 2x – 3y ≤ 6 First we solve 2x y ≥ 4 Lets first draw graph of 2x y = 4 Putting x = 0 in (1) 2 (0) y = 4 0 y = 4 y = 4 Putting y = 0 in (1) 2x (0) = 4 2x = 4 x = 4/2 x = 2 Points to be plotted are (0, 4), (2 Solve The Following Differential Equation 1 1 3 Y X Dy Dx Y 3 X 1 2 Ln X Y X Dx Ln X Dy 3 X 2 Y 2 Y 4sin X Dx 2xy 4y 3cos X Dy 4 Tan X 8sin X Sin Y Dx 8cos