MXB100 Introductory Calculus And Algebra Assignment

Question 1 (10 marks) <!--/strong-->

Find dy/dx for each of the following expressions.

1. y = (x² ? x)e^2x
2. y = cos(4/x²+ 2x⁴
3. y = 3x² + 6x + sin(x)/2e^x+1
4. 3x²y + e^y = 2 (x + 1)
5. y = (2x)^?x , note that ?x = x^1/2

Question 2 (11 marks)

Calculate the following integrals.

Question 3 (4 marks)

Mike is driving on a long, straight road with a speed limit of 100 km/hr. There is a speed camera set up exactly 76 km from his starting point. Mike’s position at time t (in hours), can be described by the function,
M(t) = 39t² + 5t,
where M(t) is his distance (in km) from his starting point.

1. What is Mike’s speed after 1 hour?
2. How fast is Mike travelling when he passes the speed camera? Will he get a speeding fine?

Question 4 (5 marks)

Kate is making a vase that is 5 cm tall, with a side profile that can be described by the equation,
y = 4? xe^?0.1x2

The figure below shows the vase’s side profile.

What is the volume of the vase?

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