## 55 Reputation

0 years, 178 days

## Graph the real roots...

Maple

Graph the real roots of the equation x3 + (a − 3)3x2 − a2x + a3=0 for a ∈ [0, 1].

Sol:=[solve(x^3+(a-3)^3*x^2-a^2*x+a^3=0,x)];

for i from 1 to 3 do

R||i:=unapply(Sol[i],a):

print(plot(R||i(a),a=0..1,numpoints=500)); end od:

Is there a simplier way to solve this. If not why did they choose this path?

## form of derivative ...

Maple

D[1,2](1/x);

what does this mean?

## discontinuous functions ...

Maple

How do I find where π(π₯) = (2*π₯ ^2) tan(2*π₯), is discontinuous in the interval [0,2π], and find the discontinuities. I know you need ot use the commands: discount(f(x),x), iscont(f(x),x=a..b,’open’), iscont(f(x),x=a..b,’close’) and fdiscont(f(x),x=a..b, resolution) which will help me find the list of ranges, each of width resolution, in which there appears to be a discontinuity in the function or its first derivative.However, what is next ?

## O differential equation question ...

Maple

Solve the following ODE for given initial conditions both analytically and numerically. Use the odeadvisor in DEtools package to classify the equations. Plot the explicit and numerical solutions in the range [0,20] using plot and odeplot commands. π¦ ′′(π‘) + 16π¦(π‘) = 3 sin(π π‘), for π ∈ {1,4,5,8}, π¦(0) = π¦ ′ (0) = 0

I started by:

ode := diff(y(t), t, t) + 16*y(t) = 3*sin(w*t);
/  2      \
| d       |
ode := |---- y(t)| + 16 y(t) = 3 sin(w t)
|   2     |
\ dt      /
[[_2nd_order, _linear, _nonhomogeneous]]

but how do I odeplot and how do I contribute π ∈ {1,4,5,8

## maple procedure ...

Maple

. Let π(π₯) = cos2 (π₯ 2+1) (sinπ₯+1) 2 and π(π₯) = (2π₯ 2 − 1) 3√π₯ + 2.

Write a procedure to return the tangent line of the function π(π₯) at the given point π₯ ∈ π·π.

I started by writing a regular Proc template

such as

tangent line:=proc(y);

however i am unsure if I shpuld go forwrad with using an if loop or not?

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