The multivariable function f(a, b) = 12 + 3a? + 3b? - 12a + 18b has...
showing multivariable calculus functions are differentiable
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2. Recall that by Theorem 3 of Section 14.3, a function f(x,y) is differentiable if its partial derivatives fa and fy both exist and are continuous. (a) Use this idea to show that the function f(x,y)-esin ry is differentiable. (b) Let o be a differentiable function and f(,)Jy Find the partial derivatives of f and determine whether they are continuous. Hint: The Fundamental Theorem of Calculus gives us that Ø has an...
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solve like example
Assign 7.3.25 Find all local extrema for the function f(x,y) = x3 - 12xy + y. Find the local maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. There are local maxima located at (Type an ordered pair. Use a comma to separate answers as needed.) OB. There are no local maxima. Question Hel Find all local extrema for the function f(x,y)=x°-21xy+y3. The function will have local...
(1 point) Find the partial derivatives of the function f(x, y)cos(12 3t 6) dt
Find all the critical numbers of the function. f(x) = 2x2 + 3x? - 36x + 10 O A. -2 OB. 6 O C. -3,2 OD. 3, -2
Math 32-_ Multivariable Calculus HW 3 (1) Consider the two straight lines L1 : (2-t, 3 + 2t,-t) and L2 : <t,-2 + t, 7-20 a) Verify that L1 and L2 intersect, and find their point of intersection. (b) Find the equation of the plane containing L1 and L2 (2) Consider the set of all points (a, y, z) satisfying the equation 2-y2+220. Find their intersection 0 and 2-0. Use that information to sketch a with the planes y =-3,-2,-1,0,...
2. [3 marks] Consider the function f(x,y) = log (– 2y). (a) Find the partial derivatives (b) Find an equation of the tangent (plane) to the surface of f at the point (3,1, f (3,1)).
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2. Given the function f(x, y)-x2 +y -2xy -6x - 2y 5, find the following: (a) Find the critical point(s) of the function. For full credit, show all the algebra to find these and give your answer as ordered pairs. (b) Find the second order partial derivatives and use these to find the determinant of each critical point. Then classify each critical point as a saddle point, relative minimum, or relative maximum point. 3. A wine dealer sells...
Figure 2 - 12-3A R2= 102 R1=50 R3-152 F Question 11 Questions 11 through 20 pertain to figure 2 What is the total power of this circuit? 270w 330w 180w 290w Question 12 1 Questions 11 through 20 pertain to figure 2 What is the power for resistor 1? 180w 270w 60w 90w Question 13 Questions 11 through 20 pertain to figure 2 What is the power for resistor 2? 180w 270w 60w D 90w Question 14 1 Questions 11...
2. [1 mark] Calculate the limit of the vector valued function f: ACRY-R lim G logy) 3. Consider the function :R? - R. given by Flv = 0 if if (,y) (0,0): (x,y) -(0,0) (a) (1 mark] State the definition of continuity of a function at the point. (1 mark] Then calculating the limit (by any technique of your choice) show that f is continuous at (0,0). (b) [2 marks] Find the partial derivatives and at (x,y) + (0,0). and...
[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...