Question

Show that the equation

*x*+sin*(x/*3)−8=0

has exactly one real root. Justify your answer.

Answer #1

show that the equation x^3 + e^x =0 has exactly one root

Show that the equation f(x) = sin(x) - 2x = 0 has exactly one
solution on the interval [-2,2]

Show that f(x)=x4+4x-2 has exactly one real root in
the interval [0, ∞)

Show that the equation − x^3 + e^ − x = − 4 has exactly one real
root.
Using Roller Theorem to prove this question. Please make the
writing a little bit easy to read. Thank You.

Each equation has one real root. Use Newton’s Method to
approximate the root to eight correct decimal places. (a) x5 + x =
1 (b) sin x = 6x + 5 (c) ln x + x2 = 3
**MUST BE DONE IN MATLABE AND SHOW CODE

Continuity and the derivative:
1A) Show that there exists a real root of the equation in this
interval: cos(root x) = e^x-2 [0.1]
1B) If f(x) is a continuous function (on the reals) that has
only one root at x=2, and if f(4)>0, can f(3)<0? Explain.

If a quadratic equation with one unknown x^2 + x +c =0
have real root, what is the range of c?

Use the IVT to prove that the equation e^x=10x^3+2 has at least
one real root.

Utilize Newton's Method to estimate the root of 3 sin x - x = 0
for x > 0 correct to the sixth decimal places. Show all work
below.
(Hint: start with x1 = 2)

Let p and q be two real numbers with p > 0. Show that the
equation x^3 + px +q= 0 has exactly one real solution.
(Hint: Show that f'(x) is not 0 for any real x and then use
Rolle's theorem to prove the statement by contradiction)

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