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Question 4 (1 point) Consider the ellipse. x² + xy + y2 = 3 Determine the...
BREAKING NEWS Eyeballing Ellipses Evidence that Implicit Differentiation Works The graph of x2 -xy y2 = 4 is a tilted ellipse, as shown below. Sketch the approximate tangent lines on the ellipse where the slopes of the tangent lines are (a) zero and (b) undefined by "eyeballing". Label the coordinates with your best estimate to two decimal places. Then, use implicit differentiation to determine the exact values of the coordinates. Express your answers as proper square root ratios. Use a...
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the increment Af if (r,y, z) changes from (1,2,3 (b) Compute the differential df for the corresponding change in position. What does (2,3,4) to this say about the point (1, 2,3)? ( 13y2)3 ( 1)2(y 2)2(z 3)2 with C (c) Consider the contour C = a constant. Use implicit differentiation to compute dz/Ox. Your answer should be a function of z. (d) Find the unit...
Consider the curve defined by the equation x² + xy + y2=4. The equation of the tangent line to the curve at the point (-2,2) is (show work)
1. Express the limit as a derivative and evaluate. 17 lim 16+h-2 lim 2. Calculate y. tan x 1 + cos x y sin(cos x) y= sec(1 +x2) x cos y + sin 2y xy Use an Implicit Differentiation] 3. Find y" if x, y,6-1. [Use Implicit Differentiation] 4. Find an equation of the tangent to the curve at the given point. 121 12+ 1 [Use Implicit Differentiation] 4. Find the points on the ellipse x2 + tangent line has...
Show all work OZ. at the point: (2, In 3, 4). (i.e. Use the ax 3. (8 points) Without doing implicit differentiation , find implicit differentiation shortcut formulas you learned!) re' + ye? + 2z. In x - 2y2 = 69.11
please help me with these. Thanks. 4. Use implicit differentiation to find an equation of the tangent line to the graph y2 + In xy = 2 of at the point (e, 1) )(-5) using formula for the derivative of the inverse 5. Consider f(x) = x + 3x - 1. Find (f function. 6. Consider the following function and its inverse f(x) = x-4 f(x) = x2 +4, point (5,1) point (1,5) x20 a) Graph both functions on the...
Question 2: Implicit Function Theorem (8pts) The equation y?(y2 - xy + 1) = 1 implicitly defines a function y = g(I) around (I, y) = (1,1). The graph is provided below. Calculate g'(1). -2 1 0 Figure 1: The graph of y'(y2 - ry+1) = 1.
14. (a) Determine all possible critical point(s) of f(, y) = x2 + xy + y2 - 3.c - 6y. (b) without using the Second Order Partial Derivatives Test (SOPDT), de- termine the nature of the obtained C.P(s). (c) Check your answer in (b) through the (SOPDT). 15. Find a point on the hyperboloid 2z = x2 - y², where the tangent plane is parallel to the plane x - 3y - 2 = 1.
14. (a) Determine all possible critical point(s) of f(x, y) = x2 + xy + y2 – 3x – 6y. (b) without using the Second Order Partial Derivatives Test (SOPDT), de- termine the nature of the obtained C.P(s). (c) Check your answer in (b) through the (SOPDT).
3) (12pts) For the function S(w)=-*+r-15x a) Determine the criticul points for the function. The critical point(s) for the function are at: b) Determine the local cxtrema using the first or second derivative test. Fill in the blanks below with the appropriate critical number. If there is no max or min mark the blank with NA (not applicable). Be sure to show all work when using cither derivative test to carn full credit. Local Maximum(s): Local Minimum(s): 3) Using the...