f(1,y) = x² + 4xy + y2 – 2.c + 2y +1. f(x,y) has a horizontal tangent 1. Find all points (a,b,c) where the graph z = plane (parallel to the xy-plane). 0 has a horizontal 2. Find all points (a,b) where the level curve f(x,y) tangent line (parallel to the z-axis).
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
Consider the paraboloid z=x2+y2. The plane 2x−2y+z−7=0 cuts the paraboloid, its intersection being a curve. Find "the natural" parametrization of this curve. Hint: The curve which is cut lies above a circle in the xy-plane which you should parametrize as a function of the variable t so that the circle is traversed counterclockwise exactly once as t goes from 0 to 2*pi, and the paramterization starts at the point on the circle with largest x coordinate. Using that as your...
2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2 at (4, 2), toward the point (7, 1). Then find the maximum slope and its direction 2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2 at (4, 2), toward the point (7, 1). Then find the maximum slope and its direction
For the limaçon x2 + y2 = (x2 + y2 - 2x)? (Exercise 24 in Section 3.5), verify that the points P(1.0) and 0(3,0) are on the graph and are the rightmost points (tangent line is vertical). (a) plug in x=1, y=0, both sides of the equation are equal to (b) plug in x=3, y=0, both sides of the equation are equal to (c) Find y'at P(1,0): y'I=1.y=0 = (d) Find y' at Q(3,0): y'Ix=3.y=0 =
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.
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...
consider the curve described by the equation: 4x2 - 3xy + y2 = 14 at any given point on this curve, we have dy/dx = -8x + 3y / -3x + 2y your task is to find the points on the curve where the tangent line is parallel to the line y = x What is the y-coordinate of the leftmost point on the curve where the tangent line is parallel to the lone y=x
Question Completion Status: QUESTION 18 If y = In(ex?+y?) then y' = 2x (a) x2 + y2 - 27 2xx² (b) — e* + y2 - 2y - 2xe* + 2y (c) 5 x + ² (0) xy + 2x Click Save and Submit to save and submit. Click Save All Answers to save all answers. RI " - mul Take Teat r et - Discord
6. Find the equation of the tangent line at the given point. (a) x2 + y2 = 25,(-3, 4) (b) 2y - Vt = 4,(16, 2) (c) y + xy² + 1 = x + 2yº, x = 2