The evaluation of So So x y e**dxdy is 0.5 e 0.25 e - 0.5 O e - 0.25

Q: Given that Vf(10, –2) = 8i – 4j, find the directional derivative of the function f at the point (10,…

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Q: Find an equation of the curve in the xy-plane that passes through the point (2, 3) and has, at every…

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Q: (2x – 3y +1)dx – (3x + 2y – 4)dy = 0

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution of the…

Q: f the following graphs is continuous and differentiable at a and (x) if it is not…

A: We have to find the following given conditions according to the given

Q: Let a = ci + jand b = 8i + 40j. Find c so that a and b are orthogonal. c = i

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Q: Use the Mean Value Theorem to show that f(r) = 2x sinh(x – 1) + 2" – x %3D has a critical number…

A: Given: We can see that the function is continuous in [0, 1] and differentiable in (0, 1). So, the…

Q: th (a) Write a nonrecursive formula for the n term of the arithmetic sequence a based on the given…

A: We need to write a non-recursive formula.

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: sin40 Prove 8cos 0 – 4cos0, show preliminaries to perform sino

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Q: Find an equation of the plane pirpendicular to the line through (2,2,-4) and (9, "1, 3) and…

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Q: 6. 9. 6, If f(x) dx = 31 and g(x) dx = 18, find [4f(x) + 5g(x)] dx.

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Q: 17. Obtain the family of solutions and particular solution of the homogeneous equation, y?dx + (x2 +…

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Q: Evaluate the integral using Integration by Parts. (Use symbolic notation and fractions where…

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

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Q: 13. dx = + C 2 6.

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Q: The integral of the given function csc x dx is equal to 3cos' x-10sinx cos'x-15sin xcOsx 15sin'x…

A: To evaluate the given integral.

Q: dx 3. 5 Sinux

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Q: Find the speed over the path r(t) = (sin(3t), cos(6t), cos(3t)) at t = (Use symbolic notation and…

A: The path r(t)=sin(3t),cos(6t),cos(3t) at t=π2

Q: Find the directional derivative of f at P in the direction of a. f (x, y, z) = xy + z²; P(3,4,–4); a…

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Q: Find equutiuns Ofthe followicy t. 9 tangent Aane b) The nomauf line

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Q: 4. dx + (x – y + 2)?dy = 0

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Q: 5 In(3x) dx 5ln (3x) +C 12. 4

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Q: 5x-20 50

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Q: 3. Given that 3e¬4rt + 2se" – 4w²rt = 3. aw (a) Find using implicit differentiation. at (b) Find at…

A: “Since you have posted a multiple question, we will solve first question for you. To get remaining…

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

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Q: 1. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of…

A: The Lagrange multipliers method is a strategy for finding local maxima or minima of a function using…

Q: 3 4. f(x) = x - 5 A. x = -1 B. x = 2

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

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Q: Let g be a function that is defined for all x, x # 2, such that g(3)% = 4 and the derivative of g is…

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Q: Find the vector component of v = (4, – 1, 7) along b = (6, 6, –7) and the vector component of v…

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Q: Test the series below for convergence using the Ratio Test. 0.7" n=1

A: Given,  ∑n=1∞n40.7n

Q: Find Duf at P. f(x, y, z) = 4x'y'z"; P(1, –2, 1); u = + %3D Duf i -Tem

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Q: Find the directional derivative of the function at P in the direction of v. h(x, у, 2) %3D хуz, P(4,…

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Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 5+t and L2 : x = 1+ 2t, y = 3 – 4t, z = 5 – 2t are…

A: To show that the lines L1: x=4-t, y=2t, z=5+t and L2: x=1+2t, y=3-4t, z=5-2t are parallel and to…

Q: 2sinx if 2 sin x %3D what is u?

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Q: -3/2 dx S(35 + 4x – 4x²)

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Q: Consider the series Σ (ӕ — аn 3 (х — 8)2 + - 8)4 (x – 8)6 + 25 - 3! (х — 8)8 125 · 4! +... 5- 2!…

A: Here, the given series is: ∑n=n0∞an=(x-8)2+(x-8)45×2!+(x-8)625×3!+(x-8)8125×4!+...…

Q: Let T3 be the Maclaurin polynomial of f(x) = e*. Use the Error Bound to find the maximum possible…

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Q: Find the distance between the parallel planes – 2x + y +z = 0 and 10r – 5y – 5z – 11 = 0. Note:…

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Q: Consider the function f(x, y) = 2x² – 7y² subject to the condition x? + y = 25. Use Lagrange…

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Q: Determine whether the series converges. Σ Vk+ 3 k=1 The series converges. The series diverges.

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Q: Determine whether the series converges using the limit comparison test. 4k2 – 2k +9 Σ 20k7 + k – 20…

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Q: Verify that y = cos x and y = sin x are solutions of the DE y” + y = 0. Are any of the following…

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Q: Find the value of x if mz1 = x mz2 = 2x – 10 mz3 = 2x + 10

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Q: Let g be a function that is defined for all x, x# 2, such that g(3)% = 4 and the derivative of g is…

A: Solved below

Q: 2. Use the Mean Value Theorem to show that f(r) = 2x sinh(x – 1) + 2" – x has a critical number…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Solution is here

Q: diong the X-dXIS WiLII all dll and t is in seconds. If you know that the initial velocity is 6 m/sec…

A: According to our company's guidelines I can only answer first three subparts of the question. For…

Q: Consicler the functiun belou 2. fexy)=x°ewy %3D a) evaluate f(8,0) b) fincd the clonain of F ) Find…

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Q: Find parametric and symmetric equations for the line satisfying the given conditions. Through the…

A: Given query is to find the parametric and symmetric equation.