1. A function of two variables is givenf(x, y) = x² + y² + e-(x²+y²)a) Draw a picture of the graph of the function f. Use for example Geogebra.b) Find a tangent plane to the graph of the function f at all points(x, y, f(x, y))c) At what points is the tangent plane parallel to the xy-plane? How does thefunction behave near the points (0, 0)?

The given function is fx,y=x2+y2+e-x2+y2. The equation of the tangent plane at a point…

Answered: 1. A function of two variables is given…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let W1 and W2 be two subspaces of a finite dimensional vector space V over a field F.The formula dim⁡(W1)+dim⁡(W2)−dim⁡(W1∩W2)=dim⁡(W1+W2), is reminiscent of the simple combinatorial formula#S1+#S2−#(S1∩S2)=#(S1∪S2).How might you deduce t from the formula dim⁡(W1)+dim⁡(W2)−dim⁡(W1∩W2)=dim⁡(W1+W2),
2. Determine the equations of all tangents to the relation (x-3)² 4 = 1 where x = 2
The figure shows the graphs of three functions: f, f', and f". Identify each curve and write which of the a), b) or c) they represent: f = f' f" a 8. 10
Consider the function defined by f(x, y) = 4x² + y². (a) Find the domain and range of f. (b) Draw a contour map of f for k –1,0,1, 2, 3. (c) Using part (b), provide a sketch of the graph of f.
explain this problem step by step
Must set up equations and use derivatives to show work please
Must set up equations and use derivatives to show work please
Consider the function defined by f(x, y) = y + √x+2. (a) Find the domain and range of f. (b) Draw a contour map of f for k=-1,0,1. (c) Sketch the graph of J.
#8.) Determine the slope of the tangent at point (1,4) on the graph of f(x) = (9-x²) ²3/ #10.) a) Determine the values of x where the graph of each function has a horizontal tangent i> y=(x²-435 -ii) y= (x³ -x)² to x + 5y -10 = D. #12.3 A tangent to the parabola y=3x²-7x +5 is perpendicular Determine the equation of the tangent. #13.) The line y = 8x tb tangent to the curve y² 2x². Determine the point of tangency and the value of b #29. Find numbers a, b, and c so that the graph of f(x) = ax² + bx tc has and a tangent with Slope 16 where x = 2 x-intercepts at (0,0) and (8.0)

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