10ExerciseConsider the function f : x → sin(x) /x. Compute first the value of f at the point x = 1.23, and then the derivative f′(x).Why does the following input not yield the desired result?f := sin(x)/x: x := 1.23: diff(f, x)
11Exercise De l’Hospital’s rule states that Compute by applying this rule interactively. Use the function limit to check your result.
12ExerciseDetermine the first and second order partial derivatives of f1(x1, x2) = sin(x1 x2) .Let x = x(t) = sin(t), y = y(t) = cos(t), andf2(x, y) = x2 y2.Compute the derivative of f2(x(t), y(t)) with respect to t.
19Integration with Real Parameters Use assume to set attributes of parameters.
20Exercise Compute the following integrals: Use MuPAD to verify the following equality:
21ExerciseUse MuPAD to determine the following indefinite integrals:
22ExerciseThe function intlib::changevar performs a change of variable in a symbolic integral. Read the corresponding help page. MuPAD cannot compute the integralAssist the system by using the substitution t = sin(x). Compare the value that you get to the numerical result returned by the function numeric::int.
29Putting All TogetherDisplay the findings about the function.
30Key Takeaways Now, you are able to find limit with optional left, and right approaches,get derivatives of functions and expressions,analyze functions by finding their asymptotes, maxima and minima,and to get definite and indefinite integrals of arbitrary functions.
31Notes limit(f(x),x=infinity) diff(sin(x^2)^2,x) hold(expr) f := x -> x^2*sin(x)reset()f'(x)D([1,2],f)limit(1/x, x=0, Right)PIint(sin(x),x=0..PI)assume(a>0)int(x^n,x) assuming n <> -1sum(k^2,k=1..n)sum(x^n/n!,n=0..infinitysimplify(expr)numer(expr)denom(expr)solve(expr)op(sol,[2,1,1])plot::Line2d([x1,y1],[x2,y2])plot::PointList2d( [[x1,x2],..])