Maple- Approximation to the smallest positive solution

Question

Part of my first year university degree, I need to work with the Maple software.

I have this question.

Find an approximation to the smallest positive solution to

$$(-38/25)*sin(9/10*x)=(13/25)*exp(-16*x/25)$$

Correct to 10 sig.figs

No matter what I do, I don't seem to get the correct answer.

Initially, I got a negative answer but then I sent the bound of x from 0 to infinity. Still getting the wrong answer.

This is my best attempt so far.

fsolve((-38/25)*sin(9/10*x)=(13/25)*exp(-16*x/25),x,x=0..infinity);

10.47244230

All help is greatly appreciated

Answer 1

restart;
expr1 := -38/25*sin(9/10*x):
expr2 := 13/25*exp(-16/25*x):

P1 := plot(expr1,x=0..10,color=blue):
P2 := plot(expr2,x=0..10,color=red):
plots:-display(P1,P2,view=-2..2);

The purpose of creating the plot is to allow you visually discover a range for x between which the two curves intersect only once.

For example you can see that they intersect only once between x=0 and x=5.

Thus you can figure out, by visual inspection of the plot, a suitable range to use when calling fsolve.

fsolve(expr1-expr2, x=0..5);

                      3.530355063

Here are some other ways,

RootFinding:-NextZero(unapply(expr1-expr2,x), 0.0);

                      3.530355062

Student:-Calculus1:-Roots(expr1-expr2, x=0..10, numeric);

               [3.530355063, 6.976944937]

min(%);

                      3.530355063