Feel free to ask for any doubt, i have mentioned product rule
that i used.
6) a (15 pts) Find the derivative of (x,y,z-xy, + x3yz + z3yx in the direction of v -2 -4k at the function fix.y z) at the point vo Can you find any direction(s) where the surface is neither increasing nor decreasing? e point vo (2, 1, -3). What is the rate of maximal increase to the b. (10 pts) Find a normal vector and the tangent plane to the following level surface x'y t yz+2 3 at (1, 1,...
6/29/2020 Prof Gutzler 4. (15 pts] (a) Solve for y(x) = x - y, y(0) = 1. (b) Use Euler's Method with step size h = 0.1 to approximate y(0.3). (c) Find the percent error in your approximation. % error = 100 y(0.3) - y y(0.3) 0,57 |
Question 1. (15 pts) Given f(x,
y) = 3x 2 + y 3 . (a) Find the gradient of f. (b) Find the
directional derivative of f at P0 = (3, 2) in the direction of u =
(5/13)i + (12/13)j.
Question 1. (15 pts) Given f(L,y) = 3x2 +y?. (a) Find the gradient of f. (b) Find the directional derivative off at P =(3,2) in the direction of u=(5/13)i + (12/13)j.
6. (5 pts) y = 6 + 3x (a) Find at least two pairs of x and y. (b) Graph the linear equation. 7. (5 pts) y = 10 - 2x (a) Find at least two pairs of x and y. (b) Graph the linear equation.
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0 < y < 2, f(z,y) (a) [6 pts] Determine if X and Y are independent. (b) [6 pts] Find P{X+Y <1) B( (c) [6 pts) Find
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0
6. Given the equation: y = x2 + 4x + 3 a. (3 pts) Find the vertex b. (3 pts) Find two other points on the parabola and graph the equation on the grid below 7. (4 pts) Graph the following linear equation on the grid below: y = x-5 3
6. (5 pts) (a) Find at least two pairs of x and y. (b) Graph the linear equation. 7. (5 pts) (a) Find at least two pairs of x and y. (b) Graph the linear equation.
Question 5. (15 pts) Find the maximum and minimum of S(,y) 22 + y2 = 1. on the circle
5) (15 pts) Find the surface area of the surface generated by revolving the curvey 0 < x < 2; about the x-axis. (HINT: S.A 6) (15 pts) Find the length of the curve y = * - 4xfrom x = 1 to x = 2.
Question 5. (15 pts) Find the maximum and minimum of f(t,y) = ry? on the circle x2 + y2 = 1