MT 129 Arab Open University Calculus and Probability Discussion

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Q?1: [3×2 marks] Let and.

a)Find. Simplify your answer.

b)Describe the domains ofand.

c)Find .

Q?2: [3×2 marks] Let and.

a)Find , express the answer as a rational function.

b)Find .

c)Find such that .

Q?3: [3+3 marks]

• Find equations of the tangent lines to the curve that are parallel to the line .

b)At what point on the curve is the tangent line parallel to the line .

Q­?4: [3+3 marks]

• Let . Use the definition of the derivative to find .
• Find the points on the graph: where the tangent line is horizontal.

Q­?5: [3+2 marks]

• Let . Find the intervals on which is increasing and the intervals on which is decreasing, if any.
• Sketch a possible graph of a function that satisfy the following conditions:

i. and .

ii., .

iii., .

Q?6: [5 marks] If the sum of the radius () and height () of a cylinder is 3 m, find the dimensions of the cylinder that maximize its volume (), .

Q­?7: [3+3 marks]

• Solve for : .
• Find an equation of the tangent line to the curve at the point whose -coordinate is 1.