By Christopher T.J. Dodson, Elizabeth A. Gonzalez
ISBN-10: 3540592849
ISBN-13: 9783540592846
ISBN-10: 364279758X
ISBN-13: 9783642797583
This e-book is designed to be used at school laptop labs or with domestic desktops, operating the pc algebra approach Maple, or its pupil model. It helps the interactive Maple worksheets that we have got constructed and that are on hand for free from a number of websites. for instance seek advice the nameless ftp website ftp.utirc.utoronto.ca (/pub/ednet/maths/maple), or the college of Toronto tutorial and study Computing world-wide-web domestic web page (hhtp://www.utirc.utoronto.ca/home.html), over the web. the subjects continue during the complete arithmetic syllabus for the 2 senior years, from easy algebra, features and sequences, to calculus and its extra explanatory textual content, solutions to routines, cross-referencing, bibliography and index.
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Additional info for Experiments In Mathematics Using Maple
Example text
F:=x->3*x-2-6*x-2; f:= x -t 3x 2 - 6x - 2 > plot(f(x),x=-2 .. 3(a), the coordinates of the minimum can be estimated to be (1, -5). 3. (a) The graph of f(x) = 3x 2 - 6x - 2, on [-2,2]. (b) The graph of y = x 2 + 4x + 9, on [-4,0] q:= -5 3 (x - 1)2 - 5 We expand the above equation to be sure that it is the same equation we started with, f(x) = 3x 2 - 6x - 2. 2 Convert the equation f( x) = x 2 + q using the graphical method. 3(b)) and estimate the coordinates of the vertex. > f:=x->x-2+4*x+9; f:=X--+X2+4x+9 > plot(f(x),x=-4 ..
F := x -t x2 - 3x +2 > plot(f(x),x=-1 .. 1. The graph of f(x) = x 2 - 3x > root [2J ; + 2, on [-1,3] 1 Of course, the easiest way to find the roots of an equation in Maple is to solve it directly. 1 Determine the roots of the function y = 2x 2 - x-I graphically. 2 Determine the roots of the following functions using any method. 3 b, c. 4 2b 2 = 9ac. 1 Completing the square of x 2 + 2x - 8 we get (x + 1)2 - 9 so the roots are given by (x + 1) = 3 and we find them to be x = -4 and x = 2. Apply the same procedure to ax 2 + bx + c and deduce the formula for solving quadratics.
T:=textplot([[10,25,'f(x)'],[10,100,'g(x)'],[10,620,'g(f(x))']], > align=RIGHT): > p:=plot({f(x),g(x),(g~f)(x)},x=-10 .. 10): > display({t,p}); In general, f(g(x)) is not equal to g(J(x)). Indeed, not often do both exist. 14. 15. (a) The graphs of inverse functions f(x) and g(x). 9 Given f(x) = 8x - 7 and g(x) = x 2 + x, find f(g(x)), g(J(x)), and f(J(g(x))). 10 Let f(x) = X 1/ 3 and for -1 :::; x :::; 1. Consider the iterated functions h(x) = f(x), f2(X) = f(h(x)), fa(x) = f(h(x)), ... Show that each of these new functions maps the interval [-1,1] to itself and plot their graphs for n = 1,2, ...
Experiments In Mathematics Using Maple by Christopher T.J. Dodson, Elizabeth A. Gonzalez
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