Student[Calculus1] - Maple Programming Help

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Student[Calculus1]

 ShowSolution
 show all the steps in the solution of a specified problem

 Calling Sequence ShowSolution(p, opts)

Parameters

 p - (optional) posint or a calculus1 problem; the problem to solve opts - (optional) options of the form keyword=value, where keyword is one of showrules, maxsteps, searchoptimal.

Description

 • The ShowSolution command is used to show the solution steps for a Calculus1 problem, that is, a limit, differentiation or integration problem such as can be expected to be encountered in a single-variable calculus course.
 • If p is omitted, the current (most recently referenced) problem is solved.  Otherwise, the problem referenced by p is solved.  A problem can be referenced either by its problem number (see GetProblem and ShowIncomplete) or by the problem itself, for example via a label.
 • The options can be used to control how the problem is solved and what is displayed.  The options are:
 – showrules = truefalse (default: true)

Normally, the rule applied at each step of the solution is displayed; if this option is given as showrules=false, the rules are not shown.

 – maxsteps = posint (default: 25)

This puts a limit on the number of rules which can be applied to solve a problem.

 – searchoptimal = truefalse (default: true)

The default behavior is to try to determine the shortest solution sequence. If this option is given as searchoptimal = false, the first solution discovered will be displayed.

 • If you set infolevel[Student] := 1 or infolevel[Student[Calculus1]] := 1 (see infolevel), Maple may display some additional, useful information about the state of the problem and its solution.

Examples

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{Calculus1}]\right):$
 > $\frac{{ⅆ}}{{ⅆ}x}\left({x}^{2}\mathrm{sin}\left(x\right)\right)$
 $\frac{{ⅆ}}{{ⅆ}{x}}{}\left({{x}}^{{2}}{}{\mathrm{sin}}{}\left({x}\right)\right)$ (1)
 > $\mathrm{ShowSolution}\left(\right)$
 $\begin{array}{cccc}\multicolumn{4}{c}{\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\left({{x}}^{{2}}{}{\mathrm{sin}}{}\left({x}\right)\right)}\\ \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}& {\text{=}}& \frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\left({{x}}^{{2}}\right){}{\mathrm{sin}}{}\left({x}\right){+}{{x}}^{{2}}{}\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{sin}{}\left({x}\right)\hfill & \phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left[{\mathrm{product}}\right]\\ \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}& {\text{=}}& {2}{}{x}{}{\mathrm{sin}}{}\left({x}\right){+}{{x}}^{{2}}{}\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{sin}{}\left({x}\right)\hfill & \phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left[{\mathrm{power}}\right]\\ \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}& {\text{=}}& {2}{}{x}{}{\mathrm{sin}}{}\left({x}\right){+}{{x}}^{{2}}{}{\mathrm{cos}}{}\left({x}\right)\hfill & \phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left[{\mathrm{sin}}\right]\end{array}$ (2)
 > ${∫}{\mathrm{sin}\left(x\right)}^{2}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}x$
 ${∫}{{\mathrm{sin}}{}\left({x}\right)}^{{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}$ (3)
 > $\mathrm{Hint}\left(\right)$
 $\left[{\mathrm{rewrite}}{,}{{\mathrm{sin}}{}\left({x}\right)}^{{2}}{=}\frac{{1}}{{2}}{-}\frac{{1}}{{2}}{}{\mathrm{cos}}{}\left({2}{}{x}\right)\right]$ (4)
 > $\mathrm{Rule}[]\left(\right)$
 ${∫}{{\mathrm{sin}}{}\left({x}\right)}^{{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}{=}{∫}\left(\frac{{1}}{{2}}{-}\frac{{1}}{{2}}{}{\mathrm{cos}}{}\left({2}{}{x}\right)\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}$ (5)
 > $\mathrm{ShowSolution}\left(\right)$
 $\begin{array}{cccc}\multicolumn{4}{c}{{\int }{{\mathrm{sin}}{}\left({x}\right)}^{{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}}\\ \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}& {\text{=}}& {\int }\left(\frac{{1}}{{2}}{-}\frac{{\mathrm{cos}}{}\left({2}{}{x}\right)}{{2}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}\hfill & \phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left[{\mathrm{rewrite}}{,}{{\mathrm{sin}}{}\left({x}\right)}^{{2}}{=}\frac{{1}}{{2}}{-}\frac{{\mathrm{cos}}{}\left({2}{}{x}\right)}{{2}}\right]\\ \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}& {\text{=}}& {\int }\frac{{1}}{{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}{+}{\int }{-}\frac{{\mathrm{cos}}{}\left({2}{}{x}\right)}{{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}\hfill & \phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left[{\mathrm{sum}}\right]\\ \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}& {\text{=}}& \frac{{x}}{{2}}{+}{\int }{-}\frac{{\mathrm{cos}}{}\left({2}{}{x}\right)}{{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}\hfill & \phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left[{\mathrm{constant}}\right]\\ \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}& {\text{=}}& \frac{{x}}{{2}}{-}\frac{\left({\int }{\mathrm{cos}}{}\left({2}{}{x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}\right)}{{2}}\hfill & \phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left[{\mathrm{constantmultiple}}\right]\\ \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}& {\text{=}}& \frac{{x}}{{2}}{-}\frac{\left({\int }\frac{{\mathrm{cos}}{}\left({u}\right)}{{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{u}\right)}{{2}}\hfill & \phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left[{\mathrm{change}}{,}{u}{=}{2}{}{x}{,}{u}\right]\\ \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}& {\text{=}}& \frac{{x}}{{2}}{-}\frac{\left({\int }{\mathrm{cos}}{}\left({u}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{u}\right)}{{4}}\hfill & \phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left[{\mathrm{constantmultiple}}\right]\\ \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}& {\text{=}}& \frac{{x}}{{2}}{-}\frac{{\mathrm{sin}}{}\left({u}\right)}{{4}}\hfill & \phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left[{\mathrm{cos}}\right]\\ \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}& {\text{=}}& \frac{{x}}{{2}}{-}\frac{{\mathrm{sin}}{}\left({2}{}{x}\right)}{{4}}\hfill & \phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left[{\mathrm{revert}}\right]\end{array}$ (6)
 > $\mathrm{Understand}\left(\mathrm{Int},\mathrm{c*},\mathrm{revert}\right)$
 ${\mathrm{Int}}{=}\left[{\mathrm{constantmultiple}}{,}{\mathrm{revert}}\right]$ (7)
 > $\mathrm{ShowSolution}\left({∫}\frac{1}{4{x}^{2}+4x+1}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}x\right)$
 $\begin{array}{cccc}\multicolumn{4}{c}{{\int }\frac{{1}}{{4}{}{{x}}^{{2}}{+}{4}{}{x}{+}{1}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}}\\ \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}& {\text{=}}& \frac{\left({\int }\frac{{1}}{{{u}}^{{2}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{u}\right)}{{4}}\hfill & \phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left[{\mathrm{change}}{,}{u}{=}{x}{+}\frac{{1}}{{2}}{,}{u}\right]\\ \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}& {\text{=}}& {-}\frac{{1}}{{4}{}{x}{+}{2}}\hfill & \phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left[{\mathrm{power}}\right]\end{array}$ (8)