Please write legibly and write what you did in each step.
Thanks
Please write legibly and write what you did in each step. Thanks 8. For the sequence {an) defined recursively by an 2-1 8. For the sequence {an) defined recursively by an 2-1
Consider the sequence {an} defined recursively as: a0 = a1 = a2 = 1, an = an−1+an−2+an−3 for any integer n ≥ 3. (a) Find the values of a3, a4, a5, a6. (b) Use strong induction to prove an ≤ 3n−2 for any integer n ≥ 3. Clearly indicate what is the base step and inductive step, and indicate what is the inductive hypothesis in your proof.
please simply. for a1,a2,a3,a4, & a5 Write the first five terms of the sequence defined recursively. Express the terms as simplified fractions when applicable. 9,- -4,a,=2a 1.5 a 1 04 as-
Please do b,c, and d. please write step by step and write legibly. thank you. 2. Definition of Derivative a) Find the slope of the tangent line to the parabola f(x) = 4x - 32 at the point a using the definition of derivative. b) Find the equation for the tangent line to f(x) = 4.c - zº if f(1) = 3. c) Find the slope of the tangent line to f(x) = (2x2 - 4) at the point a.
Write the first five terms of the geometric sequence defined recursively. Find the common ratio and write the nth term of the sequence as a function of n. (nth term formula: An = a1(r)-1) 1 a1 = 625, ak 11 = 5 -ak aj = a2 a3 = 04 = Preview 05 Preview r = Preview an = Preview Find the 6th of the geometric sequence: {64a( – b), 32a( – 36), 16a( – 96), 8a( – 27b), ...} an...
IMPORTANT: Step by step *typed* format preferred. If hand written, please write clearly and legibly. Please be sure answer is CORRECT. Thanks! How fast must a meter stick be moving if its length is observed to shrink to 0.7 m?
2. (6 points) (a) (3 points) The following recursively defined sequence is sin Sequence: ai = 0, Az = a= 1, and an+1 = an - 3an-1 + an-2 for n ? 3. Calculate the 4th, 5th, and 6th terms of this sequence.
Given the sequence an defined recursively as follows: an 3an-1+2 for n 2 1 Al Terms of a Sequence (5 marks) Calculate ai , аг, аз, а4, а5 Keep your intermediate answers as you will need them in the next question. A2 Iteration (5 marks) Using iteration, solve the recurrence relation when n21 (i.e. find an analytic formula for an). Simplify your answer as much as possible, showing your work and quoting any formula or rule that you use. In...
Step by step typed format preferred. If hand written, PLEASE write clearly and legibly. Thanks! 5. (20 pts) Show that (x3) 0 for a simple harmonic oscillator wave functions with unspecified n. (Hint: Use Symmetry properties of the Hermite Polynomials) a. (15 pts) a. Show that the solution to the free particle Schrodinger equation dx is: ψ Ae-ikx + Beikx where k = b. (5 pts) Which term vanishes (blows up) if the particle for xO region. (note: k >0)
Let the sequence X be defined recursively by x1 = 1 and Xn+1 = Xn + (-1)-1 for n 2 1. Then X n is a decreasing sequence. an increasing sequence. a Cauchy sequence either increasing or decreasing. QUESTION 12 Check if the following statement is true or false: COS n The sequence is divergent. True False
Xo Xo Problem 1. Show that the recursively-defined sequence x*i-x, - gives the sequence of x-values described in this procedure, as follows: (a) Write the linear approximation 1 (x) to the curve at the point (Xn,f(xn). (b) Find where this linear approximation passes through the x-axis by solving L(x)0 for x. xn + 1-1,-I n). is the recursion formula for Newton's Method. : Xo Xo Problem 1. Show that the recursively-defined sequence x*i-x, - gives the sequence of x-values described...