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Student[Calculus1]

  

ShowSolution

  

show all the steps in the solution of a specified problem

 

Calling Sequence

Parameters

Description

Examples

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

withStudent[Calculus1]:

ⅆⅆxx2sinx

ⅆⅆxx2sinx

(1)

ShowSolution

ⅆⅆxx2sinx=ⅆⅆxx2sinx+x2ⅆⅆxsinxproduct=2xsinx+x2ⅆⅆxsinxpower=2xsinx+x2cosxsin

(2)

∫sinx2ⅆx

∫sinx2ⅆx

(3)

Hint

rewrite,sinx2=1212cos2x

(4)

Rule[]

∫sinx2ⅆx=∫1212cos2xⅆx

(5)

ShowSolution

sinx2ⅆx=12cos2x2ⅆxrewrite,sinx2=12cos2x2=12ⅆx+cos2x2ⅆxsum=x2+cos2x2ⅆxconstant=x2cos2xⅆx2constantmultiple=x2cosu2ⅆu2change,u=2x,u=x2cosuⅆu4constantmultiple=x2sinu4cos=x2sin2x4revert

(6)

UnderstandInt,`c*`,revert

Int=constantmultiple,revert

(7)

ShowSolution∫14x2+4x+1ⅆx

14x2+4x+1ⅆx=1u2ⅆu4change,u=x+12,u=14x+2power

(8)

See Also

Calculus1

GetProblem

infolevel

label

ShowIncomplete

ShowSteps

 


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