Let F = < 3(x + 2)², 3 cos(x) + yz — 36y, — (z − 6y)² + ey > . Calculate the divergence of F and - - find point P where div(F) = 0. P=

Q: IT ) Verify that ,0) is a critical point of f(x, y) = y² - 2y cos x. Then use the second derivative…

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Q: kh= •a+h [ath 2xƒ(1) √ √ 1 + (ƒ' (1))² dt 2лf(t).

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Q: Use the second-derivative test to show that the function f(x, y) = x²eY – y²e* has a saddle point at…

A: A point (a,b) of function f(x,y) is said to be the saddle point if it is a critical point…

Q: Find y as a function of t if 16y" + 16y + 4y = 0, and y(1) = 2, y'(1) = 3. y =

A: The given differential equation  and the initial conditions .The objective is to find the solution…

Q: Compute the derivative for r(t) = d dt f(t) = (Use symbolic notation and fractions where needed.)…

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Q: If F(t) = 2xyi + xyz2j + ex+yk, then what is the divergence of F? Select one: A. 2yi + xz2j + ex+yk…

A: The divergence of a vector F=P,Q,R is given by div F=∂P∂x+∂Q∂y+∂R∂z. The given vector is Ft=2xy…

Q: Let f(x)= sec(x), find the linear approximation at x= pi/4 and use it to estimate sec(pi/5)

A: Given function: fx=secx At x=π4 fπ4=secπ4=2

Q: Let T= f(x,y) be the temperature at the point (x, y) on the circle and suppose that on the circle x…

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Q: Let y = f(x) be implicitly defined by xsin y = ycos x. Compute y' in terms of x and y.

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