b) Let f : [0, ∞) → R satisfy the ordinary differential equation f'(x) = 2+ cos f(x) with initial data f(0) = 0. You may assume this function exists and is unique. (i) Prove that, for all x = [0, ∞), x ≤ f(x) ≤ 3x. (ii) Prove that the function f has infinitely many inflexion points, that is, points where its second derivative changes sign.

Q: Suppose that f(x) is a function, whose derivative is f '(x)=(1 + cos x)(e* – 1)(x – 2)²(x – 3). At…

A:

Q: f" (x) = cos(x), f(0) = -2, f' (0) = -2, f" (0) = 6.

A:

Q: 1. Examine the continuity and differential possibilities of function f (x)= |x² – 1| in x= 1.

A: Given To check for continuity at x=1 , we find the limit to the left and right of x=1

Q: (a) Find a function f(x) satisfying the conditions f' (x) = cos(x), f(0) = -2, f' (0) = 6, f"(0) =…

A:

Q: 4. The function f(x) = 2r + cos(r) (shown right) is invertible. (a) What is the value of f-(1)?…

A:

Q: Suppose that for all real x S'(x) = -g(x) and g'(x) = f(x). (a) Show that f²(x)+g²(x)= C for some…

A:

Q: Are fi (x) = e-3* and f2(x) = e solutions to the differential equation y" – y' – 12y = 0 on the…

A:

Q: let f(x) = { ax2+x+1 if x is less than or equal to 1                 { bx if x >1   find a and b…

A:

Q: 2 (a) Consider the functions f(x) = 1– a* and F(x) =| f(t) dt. i. Write a simplified form of F(x) =…

A:

Q: -- ΣΧ E n² 22n n = 0 II

A: follow the next step

Q: Let y₁(x) and y₂(x) be any two twice differentiable functions, not necessarily eigenfunctions, in an…

A:

Q: If New Hampshire's population was 1.4 million in 2018 and there were 1.3 million motor vehicle…

A: