Maple Lab Test Solutions
> #
Ho's Maple Lab Test Solution: Semester 1 2012
(1)
# Question 1; > evalf(100*sin(95),38); 68.326171473612098369957981656827095404 > # Queston 2; > f:=x->3*sin(1/4*x^4)-sin(3/4*x)^4;
(2) > # Find 1st derivative; > D(f); (3) > # Find turning/stationary point in the interval [1,2], 1st derivative expression = 0, 10 significant figures!; > evalf(fsolve(3*cos((1/4)*x^4)*x^3-3*sin((3/4)*x)^3*cos((3/4)*x)= 0,x=1..2),10); 1.562756908 (4) > # Find 2nd derivative at x= 1.562756908; 10 significant figures!; > evalf(D[1$2](f)(1.562756908),10); (5) > # Remember to unassign variables/restart; > restart; > # Question 3; (same process as above) > f:=x-> 2^x + 2*cos(x); (6) > # Find 1st derivative; > D(f); (7) > # Find turning/stationary point in the interval [0,0.8], 1st derivative expression = 0, 10 significant figures!; > evalf(fsolve(2^x*ln(2)-2*sin(x)=0,x=0..0.8),10); 0.5201736748 (8) > # Find 2nd derivative at x= 0.5201736748; 10 significant figures! ; > evalf(D[1$2](f)(0.5201736748),10); (9) > # Remember to unassign variables/restart; > restart; > # Question 4; > eqn := x^4 + x^2*(y-1)^2 + y^4 = 4; (10)
> # to find dy/dx; > implicitdiff(eqn,y,x); (11) > > > > > > # Question 5; # a) exp(x); # b) Pi; # c) infinity; # Note the above to evaluate the definite integral; int(exp(-x)*cos(1/4*x^2)/(4+x),x=0..infinity); (12) > # Remember, % means the previous result; 10 significant figures!; > evalf(%,10); 0.1778089225 (13) > # Remember to unassign variables/restart; > restart; # Question 6; # a) arctan(x); # b) Pi; # c) sqrt (-1) = I -> Note that this is the definition of complex numbers; > # Note the above to evaluate the definite integral; > int((2+2*x^5)/arctan(x),x=3..5); > > > > (14) > # Remember, % means the previous result; 10 significant figures!; > evalf(%,10); 3702.247623 (15) > # Remember to unassign variables/restart; > restart; > > > > > > # Question 7; # a) csc(x); # b) Pi; # c) exp(x); # Note the above to evaluate the definite integral;
Ho's Maple Lab Test Solution: Semester 1 2012
(1)
# Question 1; > evalf(100*sin(95),38); 68.326171473612098369957981656827095404 > # Queston 2; > f:=x->3*sin(1/4*x^4)-sin(3/4*x)^4;
(2) > # Find 1st derivative; > D(f); (3) > # Find turning/stationary point in the interval [1,2], 1st derivative expression = 0, 10 significant figures!; > evalf(fsolve(3*cos((1/4)*x^4)*x^3-3*sin((3/4)*x)^3*cos((3/4)*x)= 0,x=1..2),10); 1.562756908 (4) > # Find 2nd derivative at x= 1.562756908; 10 significant figures!; > evalf(D[1$2](f)(1.562756908),10); (5) > # Remember to unassign variables/restart; > restart; > # Question 3; (same process as above) > f:=x-> 2^x + 2*cos(x); (6) > # Find 1st derivative; > D(f); (7) > # Find turning/stationary point in the interval [0,0.8], 1st derivative expression = 0, 10 significant figures!; > evalf(fsolve(2^x*ln(2)-2*sin(x)=0,x=0..0.8),10); 0.5201736748 (8) > # Find 2nd derivative at x= 0.5201736748; 10 significant figures! ; > evalf(D[1$2](f)(0.5201736748),10); (9) > # Remember to unassign variables/restart; > restart; > # Question 4; > eqn := x^4 + x^2*(y-1)^2 + y^4 = 4; (10)
> # to find dy/dx; > implicitdiff(eqn,y,x); (11) > > > > > > # Question 5; # a) exp(x); # b) Pi; # c) infinity; # Note the above to evaluate the definite integral; int(exp(-x)*cos(1/4*x^2)/(4+x),x=0..infinity); (12) > # Remember, % means the previous result; 10 significant figures!; > evalf(%,10); 0.1778089225 (13) > # Remember to unassign variables/restart; > restart; # Question 6; # a) arctan(x); # b) Pi; # c) sqrt (-1) = I -> Note that this is the definition of complex numbers; > # Note the above to evaluate the definite integral; > int((2+2*x^5)/arctan(x),x=3..5); > > > > (14) > # Remember, % means the previous result; 10 significant figures!; > evalf(%,10); 3702.247623 (15) > # Remember to unassign variables/restart; > restart; > > > > > > # Question 7; # a) csc(x); # b) Pi; # c) exp(x); # Note the above to evaluate the definite integral;