Difference between revisions of "Assume Command"

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(:{{example|1=<code><nowiki>Assume(x>0 && n>0,Solve(log(n^2*(x/n)^lg(x))=log(x^2),x))</nowiki></code> yields <code>{x = 100, x = n}</code>}})
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;Assume( <Condition>, <Expression> )
 
;Assume( <Condition>, <Expression> )
 
:Evaluates the expression according to the condition
 
:Evaluates the expression according to the condition
:{{example|1=<code><nowiki>Assume(a > 0,Integral(exp(-a x), 0, infinity))</nowiki></code> yields <code>1 / a</code>.}}
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:{{examples|<div>
:{{example|1=<code><nowiki>Assume(x>0 && n>0,Solve(log(n^2*(x/n)^lg(x))=log(x^2),x))</nowiki></code> yields <code>{x = 100, x = n}</code>}}
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:*<code><nowiki>Assume(a > 0, Integral(exp(-a x), 0, infinity))</nowiki></code> yields <code>1 / a</code>.
 +
:*<code><nowiki>Assume(x>0 && n>0, Solve(log(n^2*(x/n)^lg(x))=log(x^2), x))</nowiki></code> yields <code>{x = 100, x = n}</code>
 +
:*<code><nowiki>Assume(x<2,Simplify(sqrt(x-2sqrt(x-1))))</nowiki></code> yields <code>-sqrt(x - 1) + 1</code>
 +
:*<code><nowiki>Assume(x>2,Simplify(sqrt(x-2sqrt(x-1))))</nowiki></code> yields <code>sqrt(x - 1) - 1</code>
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:*<code><nowiki>Assume(k>0, Extremum(k*3*x^2/4-2*x/2))</nowiki></code> yields <math> \left\{ \left(\frac{2}{3  k}, -\frac{1}{3 k} \right) \right\} </math>
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:*<code><nowiki>Assume(k>0, InflectionPoint(0.25 k x^3 - 0.5x^2 + k))</nowiki></code> yields <math> \left\{ \left(\frac{2}{3  k}, \frac{27  k^{3} - 4}{27  k^{2}} \right) \right\} </math>
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</div>}}
  
  

Latest revision as of 15:17, 31 January 2020


CAS Syntax

Assume( <Condition>, <Expression> )
Evaluates the expression according to the condition
Examples:
  • Assume(a > 0, Integral(exp(-a x), 0, infinity)) yields 1 / a.
  • Assume(x>0 && n>0, Solve(log(n^2*(x/n)^lg(x))=log(x^2), x)) yields {x = 100, x = n}
  • Assume(x<2,Simplify(sqrt(x-2sqrt(x-1)))) yields -sqrt(x - 1) + 1
  • Assume(x>2,Simplify(sqrt(x-2sqrt(x-1)))) yields sqrt(x - 1) - 1
  • Assume(k>0, Extremum(k*3*x^2/4-2*x/2)) yields \left\{ \left(\frac{2}{3 k}, -\frac{1}{3 k} \right) \right\}
  • Assume(k>0, InflectionPoint(0.25 k x^3 - 0.5x^2 + k)) yields \left\{ \left(\frac{2}{3 k}, \frac{27 k^{3} - 4}{27 k^{2}} \right) \right\}



Note: See also Solve Command.
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