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5. Given to the right is the graph of the function f(r, y) ye/2 on the...
[Question 1] Find and graph the domain of the function f(,y)-In-) Question 2] Graph a contour map of the function f(z, y)2s y 1 that contains four level curves. Make sure to find an equation for each level curve and label each one on the graph. IQuestion 3] The equation of the tangeat plane to the function z the equation: Using the form of the equatioa above, fiud the tangent plane to f(a,y)yat the point (2. ). Question 4] Find...
5 Draw a computational graph to compute the function f(, y) ( graph to compute f (2,3) -y). Use the Draw a reverse mode graph to compute the derivatives f/0x and อ//ay for f 3( y). Use the graph to find those derivatives at 2 and 3. 6 5 Draw a computational graph to compute the function f(, y) ( graph to compute f (2,3) -y). Use the Draw a reverse mode graph to compute the derivatives f/0x and อ//ay...
1. Use methods of algebra and calculus to analyze the graph of the function$$ f(x)=\frac{-x^{3}-x+5}{2 x^{3}+3 x^{2}-7} $$Include all the following in your analysis:a) the domainb) interceptsc) equations of asymptotes (both vertical and horizontal)d) relative extrema (be sure to provide all derivatives, identify critical numbers, and show the test for those values - naming the test you are using.)e) intervals where the function is increasing or decreasingf) inflection points (be sure to identify possible inflection points and be sure to...
2. The graph of a function, f(x), is provided to the right. 2 Use this graph to answer each of the following questions. (a) You are also told that f(x) passes through (1, 0.8). -4-3-2f11 1 2 3 Find the equation of f(x), where you use the smallest degree possible. -2 (You can write your answer in factored form.) [6 pts] -3 -4 -5 -6 -7 -8 -9 (b) Based on the graph, describe the end behaviors of f(x). [2...
tl tt traRlo 2) The table below shows some values for a function questions. Use the values to answer the following 4 2 0 1 x 2.5 2.25 y-fx) 3, 4 1 a) (4 pts) Estimate f(x) dx by finding T, and illustrate your approximation on the graph of f shown at the right. y-Ax) 18 3.25 3 x 2.25 6.75 4-0 AX- b-a 2 L 2+ 3.2 = IS R, 3.2+ .s.2 = 10.5 T,18210.5 14.25 by finding M,...
Problem 3. Define the function: 2+_ 0 if (z,y)#10.0) if (a,y)-(0,0) f(x, v)= (a) Graph the top portion of the function using Geogebra. Does the function appear to be continuus at 0? (b) Find fz(z, y) and fy(z, y) when (z, y) #10.0) (c) Find f(0,0) and s,(0,0) using the limit definitions of partial derivatives and f,(0,0)-lim rah) - f(O,0) d) Use these limit definitions to show that fay(0,0)--1, while x(0,0)-1 (e) Can we conclude from Clairaut's theorem that()-yr(x,y) for...
5) The level curves of a function f(x,y) are given in the graph below. 2 X -1 -2 i Estimate f(3,3) ii Estimate Vf(-3, 1) Let u be a unit vector parallel to (1,4). Calculate Daf using your answer from i iv) Find the location of all critical points of the function f, on the set -5 <r< of these is a saddle point) iii) Let D be the domain bounded between the curves y = x and y= 2...
Problem 2. Suppose that gx, y, 2) is a function with the following properties: -1,2,-4 5, 9(-1,2,-4)-2, 9u(-1,2,-4) -3, and 9.(-1,2,-4) 6 Answer the following questions, and carefully justify all your answers. (a) Estimate the value of g(-0.8,2.1,-4.2). near y (b) In what direction from the point (-1,2, -4) does g decrease the fastest? What is the rate of change in this direction? (c) Which of the following objects exist(s)? Justify your answers, and find an equation for the ones...
Use the graph of the function f shown to the right to find (-2),(-1), and f(o). 10 R-2)=0 f(-1)=0 f(0) = -10 10 Enter your answer in each of the answer boxes.
Sketch the graph of y=f'(x) 13. Below you are given the graph of the function y(x). Use the graph to answer the questions that follow. y- . O-