Find a unit vector in the direction in which f(x, y, z) = 3x³z² + 3y³z + 24z − 5 increases most rapidly at P(2,2,−1), and find the rate of change of f at P in that direction. NOTE: Enter the exact answers. u= |||Vƒ(2, 2, −1)|| = =

Q: Let f(x) = (2x-3)/(x-1) as x --> - infinity,    f(x) --> ?

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: (x)=(x+0.9)/(1+x^(3)) oth f and its derivative on the

A:

Q: Find the volume of a pyramid with a square base, where the perimeter of the base is 4.7 cm4.7 cm and…

A: We need to find volume of pyramid for given data.

Q: Determine all value(s) of C in the table below so that the function is one-to-one. X f(x) 11 -11 -8…

A:

Q: (a) Express the length, L, of the parcel as a function of d. (b) Express the width, w, of the parcel…

A:

Q: 18 ft ladder leans against a wall. The bottom of the der is 3 ft from the wall at time t = 0 and…

A: In this problem will be using Pythagoras and the application of derivative to find the rate of…

Q: 3. Find the equation of the parabola through the point (6,-5) if its vertex is at origin and its…

A:

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answers…

A: Given function,  f(x)= 3x4 − 18x3 + x − 9 The function f(x) is concave upward on an interval I if…

Q: A model for the height h (in feet) of a Ferris wheel car is h = 70 + 70 sin(4πt), where t is the…

A:

Q: Consider the following curve. X = ==—= (y² + 2) ³/2, 3≤ y ≤5 Set up an integral in terms of y that…

A: I am attaching an image so that you understand each and every step.

Q: Suppose dy/dt= 6 ze^(3z^2+2) and y(0)=4. what is y(1)?

A:

Q: Solve the system of two linear inequalities graphically. Step 3 of 3: Select and graph the option…

A: y≤2x-4y>4x-8  To solve the two linear inequalities graphically.

Q: use linear approximation to estimate (4.01/sqrt9.02). write your answer as a simplified fraction

A:

Q: This is similar to a problem in the textbook. t (seconds) 0246 8 H+ Velocity (ft/sec) 0 481430 Shown…

A:

Q: An open box is to be made out of a 10-inch by 14-inch piece of cardboard by cutting out squares of…

A:

Q: Given that Vf(8, −11) = 9i – 8 j, find the directional derivative of the function f at the point (8,…

A:

Q: У y = -12x +4 3 X

A: y=-12x2+4x3

Q: 6. Determine a vector p with |p1=5 such that p is collinear to AB given the points A(3, -7, -1) and…

A:

Q: For what value of the Constant c is the function F defined below continuous on (-00,00)? Fly= { Y²-C…

A: A function,

Q: K Sketch the region of integration, reverse the order of integration, and evaluate the integral.…

A:

Q: A nonhomogeneous equation and a particular solution are given. Find a general solution for the…

A:

Q: Problem #3: The tangent plane of f(x,y) = 2x²y - 4xy at the point (1,1) can be expressed in the form…

A:

Q: The given curve is rotated about the y-axis. Set up, but do not evaluate, an integral for the area…

A:

Q: Sketch the graph of the given function. Identify any local extrema and points of inflection.…

A:

Q: This is similar to a problem in the textbook. Year 1950 1960 1970 1980 1990 Rate of change (million…

A:

Q: The function f(x) = x³ + bx² + c has a critical point at (-2, 6). a) Find the constants b and c. b)…

A:

Q: Question 2. Find the maximum and minimum values of the function f(x, y) xey² on the curve C, where C…

A:

Q: Express this nonsingular matrix as a product of elementary reduction matrices. 1 2 2 -1 0 3 1 T =

A: We have given a non singular Matrix and we have to express this as a product of elementary reduction…

Q: The curves 1(t) = (- 5t, t², 4t5) and r2(t) = (sin(4t), sin(- 4t), t - π) intersect at the origin.…

A:

Q: Heights of Children For children between the ages of 5 and 13 years, the Ehrenberg equation In(W)…

A:

Q: Your velocity is given by v(t)=2t^2+6 in m/sec, with t in seconds. Estimate the distance, s,…

A:

Q: You are given the graph of a function f. 0 concave downward 1 Determine the intervals where the…

A: You are given a graph of a function f. To determine the intervals where the graph of f is concave…

Q: Determine the third derivative of f(x) if ƒ(x) = 2xº −x³ +4x²2 - 2x¹ +5x-8. Use positive exponents…

A:

Q: Find the volume of the region bounded above by the surface z = 3-y² and below by the rectangle R:…

A:

Q: y = 20ce-0.08x Find the derivative of the function: y' (x) = 0 The x-intercept is x = The…

A: y=20xe-0.08x  Find the derivative of the function.

Q: Your backpacker's guide contains a grid map of London, with each unit on the grid representing 0.25…

A:

Q: Question 7 Multiple choice (one answer) Find the solution of: 3 gdy +y*ecosa sin .cdr =0 xdx O 3…

A:

Q: Set up but do not evaluate the triple integral 2 JB E exy dV where E is the solid

A:

Q: Find the inflection points and analyze concavity near the inflection point using an interval chart.

A: NOTE: Refresh your page if you can't see any equations. . take the first derivative

Q: 8. Find the parameterization of four different paths from (-1, 1) to (1,1). One should be a line,…

A:

Q: Solve the following system of equations using Gaussian elimination or Gauss-Jordan elimination. -2x…

A: Given system of equations -2x - 9y - z = 18 -4x - 6y - 2z = 12 3x + 9y + z = -17

Q: Write a formula for the distance between a point (x, y) on the graph of y = x and the point (3, 11).…

A: given y=x4point is (3,11)distance between two points (x1,y1) and (x2,y2) is D=(x2-x1)2+(y2-y1)2

Q: The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x)…

A: Given: f(x)=1.8208e0.3387x We have to find in what year exports reach $12.8 billion.

Q: Solve the following system of equations using Cramer's Rule. - 3x - 3y +z = -2 - 4x - 4y +z = -6 -…

A:

Q: Use cylindrical coordinates to find the volume of the region bounded by the plane z = √29 and the…

A: The region bounded by the palne z=29 and the hyperboloid z=4+x2+y2

Q: - sin(1-1) inches per hour, where t represents hours since 12 a.m. The water level of a certain body…

A: As per rule I need to solve only first three subparts.

Q: ind the standart equation of each parabola a. focus is at (2,0) b. directrix .x=3 c. Directrix is…

A:

Q: A hockey player skates on a line that is perpendicular to the goal line. If the line on which he is…

A:

Q: Use the graph to state the absolute and local maximum and minimum values of the function. (Assume…

A:

Q: 12/23 A book designer has decided that the pages of a book should have 1 in. margins at the top and…

A: Let printed area = A  so for the maximum printed area  either dAdx = 0  or  dAdy = 0 and  d2Adx2<…