I am emailing a link of this to everyone on the class list every Friday afternoon. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.ie and I will add you to the mailing list.

Exercise Answers

Section 1.1

Q. 8 f(1.8)\approx 16.56, f(2.25)\approx 24.75. Q. 9 f(3.5)\approx 3.75, f(5.25)\approx 13\frac{13}{16}. Q. 10 f(9)\approx 2.200, f(8.2)\approx 2.105. Q. 11 f(3.5)\approx 1.419, f(4.2)\approx 1.522. Q. 12 f(3.5)\approx 12.25, f(5.25)\approx 28\frac{1}{16}. Q. 14 10.08. Q. 15 11.44. Q. 16 f'(1.5)\approx 48, f'(1.8)\approx 76.8. Q. 17 f'(3.4)\approx 3.6 and f'(4)\approx 4.2.

Section 1.3

To check that we have the correct solutions to simultaneous equations/linear systems we can plug in our values in to ALL of the equations and see that our solution set satisfies all of the equations. Note that solving two out of three equations does not mean that we have a solution. Quite often an arithmetic slip will give us a solution set that only fails for one of the equations. Hence I give solutions to the 3\times 3 systems in terms of the coordinates (x_1,x_2,x_3).

Q. 2 (iv) \displaystyle \left(\frac19 , -\frac73 , \frac{10}{9}\right), (v) \displaystyle \left(-21-15z,-17-11t,t\right) for t\in\mathbb{R}, (vi) (-7,-9,1), (vii) \displaystyle \left(\frac12 , -\frac12 , 4\right), (viii) (2,2,-1), (ix) (0,2,-2). Q. 4 All false.