Chapter 8.3, Problem 99E

43–46. Directions of change Consider the following functions f and points P. Sketch the xy-plane showing P and the level curve through P. Indicate (as in Figure 15.52) the directions of maximum increase, maximum decrease, and no change for f. ■ 45. f(x, y) = x² + xy + y² + 7; P(−3, 3)

plese do #48

43-46. Directions of change Consider the following functions f and points P. Sketch the xy-plane showing P and the level curve through P. Indicate (as in Figure 15.52) the directions of maximum increase, maximum decrease, and no change for f. T 45. f(x, y) = x² + xy + y² + 7; P(−3, 3)

In Problems 1 and 2 find the eigenfunctions and the equation that defines the eigenvalues for the given boundary-value problem. Use a CAS to approximate the first four eigenvalues A1, A2, A3, and A4. Give the eigenfunctions corresponding to these approximations. 1. y" + Ay = 0, y'(0) = 0, y(1) + y'(1) = 0

A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…

Assume that you fancy polynomial splines, while you actually need ƒ(t) = e²/3 – 1 for t€ [−1, 1]. See the figure for a plot of f(t). Your goal is to approximate f(t) with an inter- polating polynomial spline of degree d that is given as sa(t) = • Σk=0 Pd,k bd,k(t) so that sd(tk) = = Pd,k for tk = −1 + 2 (given d > 0) with basis functions bd,k(t) = Σi±0 Cd,k,i = • The special case of d 0 is trivial: the only basis function b0,0 (t) is constant 1 and so(t) is thus constant po,0 for all t = [−1, 1]. ...9 The d+1 basis functions bd,k (t) form a ba- sis Bd {ba,o(t), ba,1(t), bd,d(t)} of the function space of all possible sα (t) functions. Clearly, you wish to find out, which of them given a particular maximal degree d is the best-possible approximation of f(t) in the least- squares sense. _ 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1 function f(t) = exp((2t)/3) - 1 to project -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5…

If a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9.   The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24?   The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by a step by step creating a chart. Clearly mark the range, identifying the…

Find the closed formula for each of the following sequences (a_n)_n>=1 by realting them to a well known sequence. Assume the first term given is a_1 d. 5,23,119,719,5039 i have tried finding the differnces and the second difference and i still dont see the pattern

Solve the differential equation by variation of parameters 3x2y" + 7xy' + y = x2 - x