Calculus Techniques – Mathematics

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14:55 apply graphical methods to the solution of two engineering problems involving exponential growth and decay, analysing the solutions using calculus
apply the rules for definite integration to two engineering problems that involve summation.

The voltage in a circuit is given by v = 60(1 —e 0.2f where t is the time in seconds. Plot a graph of voltage against time for seconds.
I. Measure the gradient at the point representing an elapsed time of 9 seconds. H. Differentiate the above expression for voltage and find the rate of change of the voltage after 9 seconds have elapsed. III. Calculate the percentage error in the value from your graph.
Task 3b
For a certain material, Newton’s law of cooling can be represented by the decay equation 0= 25 + 80e where t is the time in seconds. And 0 is the temperature at any given instant in time.
I. Plot 0 against t at 0.5sec intervals for 05! 56
II. From your graph, find the initial temperature and the temperature that the body approaches as time increases to infinity.
III. Determine the slope at t = 3 seconds both from the graph and by differentiation and give your comment as you compare the results.

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