Heffernan 2008 Exam 1 Question

[mano91]

question 7)  drawing the slope field.
can i get a hand with this as the solution isnt very good, the gradients are hard to distinguish.
let me know if you would like the question posted up

[ryley]

At any given x value, the slope will be defined by substituting that x value into the derivative function, in this case sqrt(x). As long as you clearly have the gradient equal to zero at x=0 and have the gradient gradually increasing for all other x values (as sqrt(x) increases as x does), you should be fine. My teacher is an examiner and she said that they are not too pedantic about the accuracy of the gradient itself at each point, as long as you accurately show how it changes and you don't show points of equal gradient as being too different. Quick side point, if the gradient function was in terms of x and y, you have to substitute both values to determine the gradient at a point in the plane.

[monokekie]

There are at least two past vcaa exam 1s that require you to draw slopefileds. The solutions really serve to demonstrate what are required by the examiners, as there are sample sketchings available.

Apart from digging up the vcaa ones, you may also start collecting slopefield questions from those commercial exams, and compare different types of slopefield questions as well as their sample solutions. Hopefully you will soon be able to master sketching those gradients!

[TrueTears]

Slope fields are really easy once you get to do a few more of those. I know essentials (if that's the book you are using) lacks these type of questions.

If you do a lot of exams you will come across them quite often.

[monokekie]

Quick side point, if the gradient function was in terms of x and y, you have to substitute both values to determine the gradient at a point in the plane.

I really hope this shit doesn't pop up this year its tiring as hell.

[mano91]

thank you all!
i agree with u true tears, there are only 2 or 3 questions in essentials!
same as eulers method, i need to practice that
you have all been very helpful