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Text File | 2000-04-02 | 3.6 KB | 333 lines

>13.Inequality. (Parameters) a^2≤x^2≤-2>0 MYSZEK 2xy EXAMPLE e t101 p10 t0 zr t1 p6 t0 v500 zrm k^ t2 p2 t0 ;kCm cam k^m c2m ;kSm sdm cxm k^m c2m sdm k-m c2m k>m c0m kP t4 p7 t0 Pd ca t5 p6 t0 cam p2 t6 p4 t0 Po p1 ke t7 p4 t0 kem p10 oxm kS t8 p3 t0 sgm kbm2 slm kbm k>m kd t9 p6 t0 kd t12 kd p6 t0 kdm cam k#m c0m kP kPm kY t14 p6 t0 kYm p1 slm t16 p9 t0 kbm k=m ke t18 p3 t0 kem p10 oxm t20 p4 t0 sd t22 p5 t0 sdm shm ssm spm2 ssm c0m kQ t24 p6 t0 kQm p10 oxm Pp t26 p4 t0 sd t28 p6 t0 sdm ssm spm ssm k/ t30 p6 t0 k/m klm sdm2 cam k^m c2m sdm slm3 shm ssm spm2 ssm kxm spm2 k? t32 p4 t0 k?m ox p20 oxm sgm kbm sdm spm ssm sem ssm k@ t34 p6 t0 k@m sem ssm shm ssm kc p1 kcm sem com crm kvm slm3 kbm k<m k-m ke t36 p3 t0 kem p10 oxm t38 p4 t0 spm kb t40 p5 t0 kbm kb kbm sgm shm ssm sem ssm k@ v1000 k@m sdm kbm sdm k| k|m shm k|m spm3 ssm slm ssm kcm v500 slm4 ssm slm ssm kvm ;ke ;t46 ;p3 ;t0 ;kem ;p10 ;oxm kV t42 p3 t0 kVm on p10 onm p10 oxm t44 p5 t0 kPm ze t102 p10 t0 zxm zem e q BLURB 1`We are going to solve the inequality: 1`#@a^2≤x^2≤-2>0@, 1`where "$a"$ is a parameter. 2`We open the &Equations& window and write the problem. 2`#To create an exponent we press &Shift&+&6& or 2`#the on-screen button. 4`#Using the mouse we move to 4`#the &Data and auxiliary variables& window. 4`#It is minimized now. 5`#We write the parameter: 5`#"$a$. 5`#If we have more than one parameter 5`#we place each of them in a separat line. 6`Using the mouse we move to the &Equations& window. 7`As usual after formulating the problem we press &ENTER&. 8`We transform the inequality. 9`We consider two cases: 9`#"$aπ0⁄a=0"$. 12`#We add the conditon: 12`#"$aπ0"$ 12`#to the domain 12`#(press the on-screen button or &Shift&+&D& keys). 14`#We create the second case 14`#(press &Shift&+&Y& or the on-screen button). 16`#The program copies the contents of the previous case. 16`#We have to modify the domain condition. 18`We press &ENTER& to confirm the breakdown. 20`We solve each case separately. 22`#In the &case 2& window we 22`#substitute the value for "$a"$ into the inequality. 24`#This is a contradiction. 24`#We press the &Contradiction& button. 26`Using the mouse we move to the &case 1& window. 28`#We divide both sides of the inequality by 28`#@a^2≤@. 28`#We do not reverse the inequality sign since 28`#for "$aπ0"$ we have @a^2≤>0@. 30`#To insert "$2"$ into the numerator, 30`#we mark the block 30`#and press the &"/"& button at the end of it. 32`We ask the program for a hint at the inequality sign. 34`#To insert the fraction under the root sign 34`#we mark the block and 34`#press &Shift&+&2& or the on-screen button. 34`#Notice the position of the mouse. 36`We press &ENTER& to check our solution. 38`We transform the expressions. 40`#We press the &Backspace& button twice 40`#to remove the root sign. 42`#This is the final result. 42`#We press the &Answer& button. ;42`#We press "&ENTER&" ;42`#&without making any changes& in the expression. 44`Now the problem is solved. 46`We press &ENTER& again. 101`#We show how to use 2xy. 101``#"The presentation proceeds automatically." 101``#To move yellow panels use the mouse. 101`#Press ENTER on the KEYBOARD to continue. 102`#In a moment the &Examples& window will appear. 102`You can watch the same presentation again, or 102`#load the next example, or 102`#close the window and solve your own problem.