Use the Intermediate Value Theorem and the Mean Value Theorem to
prove that the equation cos (x) = -10x has exactly one real
root.
Not permitted to use words like "Nope", "Why?", or
"aerkewmwrt".
Will be glad if you can help me with this question, will
like to add some of your points to the one I have already summed
up.. Thanks
2.a Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for all
xin an interval ( a , b ), then f is constant on ( a , b
).
b True or False. The product of two increasing functions is
increasing. Clarify your answer.
c Find the point on the graph of f ( x ) = 4 − x 2 that is
closest to the point ( 0 , 1 ).
Solve the frictionless pendulum equation use Runge- kuta 4 or
forward Euler
ly'' = -g*sin(y)
where g is gravitational acceleration and l is the length of the
pendulum. The function y(t) represents the angle of the pendulum
with respect to the vertial and y'(t0 the angular velocity. You
will need to write the second-order equation as a system of two
first-order equations, and you will need to write a function file
that will evaluate this system of equations. Plot the...
Solve the frictionless pendulum equation use Runge- kuta 4 or
forward Euler
ly'' = -g*sin(y)
where g is gravitational acceleration and l is the length of the
pendulum. The function y(t) represents the angle of the pendulum
with respect to the vertial and y'(t0 the angular velocity. You
will need to write the second-order equation as a system of two
first-order equations, and you will need to write a function file
that will evaluate this system of equations. Plot the...
Use the Cauchy Criterion to prove the Bolzano–Weierstrass
Theorem, and find the point in the argument where the Archimedean
Property is implictly required. This establishes the final link in
the equivalence of the five characterizations of completeness
discussed at the end of Section 2.6.