Suppose that f(x, y) = xy. The directional derivative of f(x, y) in the directional < 1,5> and at the point (x, y) =(4,-5) is

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Q: 4)Evaluate 2 In x 7 x² dx

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Q: can you please annotate this and show all working out

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A: given,  x=et and y=te-t(i) ddx(ex)=ex(ii)  d dx(ab)=bdadx-adbdxb2(iii)  dydx=dydtdxdt

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A: Given: a. f(x)=2e3x-3ln(2x)b. f(x)=sin2(xlnx)c. f(x)=tan(lnx2+1) We are required to find: Derivative…

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A: y= 2sin3(x-30 degrees)   simplify y= 2sin(3x-90 degrees)

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Q: Utilize Cylindrical Coordinates to construct (do not calculate) one or more integrals that show the…

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Q: A. The function f(x)=√x² + 1 has a critical point at x =

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A: Fx,y,z=yzi+xzj+xyk

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Q: 21. dy dx = X xy + y Hint: Let u = x2.

A: Question 21:We have to solve the differential equation:dydx=xx2y+y3

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Q: Suppose f(x) = √(x − 1) and g(x) = (2x − 3)/(x + 2) . (a) Find (f ◦ g)(14). (b) Find a simplified…

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Q: Verify the identity algebraically. Use a graphing utility to check your result graphically. 6 sin(x)…

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Q: 38. If i f(x) dx = 12 and f f(x) dx = 3.6, find f f(x) dx. 39. If(f(r) dr 4

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Q: A police car is located 60 feet to the side of a straight road. A red car is driving along the road…

A: Let's first assign the variables and the values:                                                  x=…

Q: Which numerical method is more accurate, the Euler method or the Runge-Kutta method?

A: Here we have to tell which method is more accurate when compare to Euler method and the Runge-Kutta…

Q: Consider points P, Q, R, and S. Suppose that u =PQ, v = QR, -59 u = RP, and 52 v = PS. a) Are P, Q,…

A: We are given points P,Q,R,S such that   u=PQ→, v=QR→, -59u=RP→, 52v=PS→ Also find order of points on…

Q: at r s) The linear () is = where A is approximation to f(x) = √√/1 + 8x y = A + Bx and where Bis

A: The given function fx=1+8x. We have to find the linear approximation of fx at x=0.

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Q: Use Green's Theorem to evaluate k F. dr. (Check the orientation of the curve before applying the…

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Q: Find the tangent line(s) at the pole for the curve r-8 sin 30, 0 s0<

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Q: Given the following matrices, find 2B - A. 8 1 - [3-49] 5 A = [1 0 -37 6-12 and B=

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: 39. If f f(x) dx = 37 and fo g(x) dx = 16, find [2f(x) + 3g(x)] dx.

A: If ∫09 f(x) dx = 37 and ∫09 g(x) dx =16 , find ∫092 f(x) + 3 g(x) dx.

Q: 2. For n > 4 one has 2n>n².

A: For n&gt;4 one has 2n&gt;n2.

Q: 30. ²₂√4 - x² dx

A: To evaluate the following integral by interpreting in terms of areas. ∫-224-x2 dx Note: Since, the…

Q: Evaluate the line integral, where C is the given curve. √xyev² dy, C: x = 2t₁ y = 3t², z=2t³, ostsi

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Q: A)    cos2theta - cos theta= 0 B)    Solve for x  2ex-1 = 14

A: Given equation  A) cos2θ - cosθ = 0

Q: y" - 4y' = -4te²t, y(0) = 0, y'(0) = 1

A: Differential equation is called the equation which contains the unknown function and its derivatives…