dv 9. S- V3v-2a 10. S(5 – 3y)*dy

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

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Q: Find the derivative of the function described. (Rx5) 1. y = (2x + 3) (5x – 4)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Remember that rectangular form is z = a + bi and that polar form is z = r(cos 0 + i sin 0) Take…

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Q: Find the vector component of v = 2i – j + 3k along b = 3i + 6j + 6k and the vector component of v…

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Q: Calculate r' (t) and T(t) and evaluate T(1). r(t) = (6+ 71,1,5 – 1²) (Give your answers using…

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Q: Use Lagrange multipliers to find the maximum and minimum values of subject to the given constraint.…

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Q: DIFFERENTIAL EQUATIONS Solve the following application problems. *show the every details of your…

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Q: (x – 3y + 3)dx + (3x + y + 9)dy = 0

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Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x– y + z =…

A: This question is based on finding direction cosine using dot product as two perpendicular plane is…

Q: . Use separable equations to find the general and particular solution of xy dx – (x +

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Q: Use the triple integral to find the volume of a solid G enclosed by surfaces x = y*2 and planes…

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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…

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Q: Find an equation of the plane that is parallel to the plane x + 3y – 8z + 18 = 0 and contains the…

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Q: What is the area of the region bounded by the graph of r2 16 cos 20? (Choose all applicable…

A: The curve r2=16 cos 2θ

Q: A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the…

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Q: Find the exact volume of the solid formed in the first octant bounded above by the cone z = 2 - /x2…

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Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Here, the given equation of the plane is 3x+y-6z=8 So, the coefficients of x,y and z will give us…

Q: 7. Differentiate the following functions. sec (x³+1) b. у 3 cos yx

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

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Q: Solve the following and show the complete solution. 1. Find Duf at P: f(x, y) = sin(8x – 5y); P…

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Q: Find the solution with the given initial condition. r"(t) = (e', sin (t), cos (f)), r(0) = (1,0, 1),…

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Q: Use spherical coordinates to show that the volume of a sphere of radius R is V = *nR³.

A: Given the radius of sphere is =R  Then equation  of sphere is                      X2 + Y2 + Z2 = R2…

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j…

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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: (a) Find an equation of the tangent plane to the surface at the given point. хуz %3D 10, (1, 2, 5)…

A: Given:  a)   The equation of surface is   F(x, y, z) = xyz – 10 = 0   given point =1,2,5 On…

Q: Let a=ci+ja=ci+j and b=9i+45jb=9i+45j. Find c so that a and b are orthogonal.

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Q: Find parametric equations of the line that satisfies the stated conditions. The line through (2, 3)…

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Q: Use Lagrange multipliers to find the indicated extrema of f subject to two constraints, assuming…

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Q: Solve for x, if ∠1 = (4x+40)   and ∠2 =  (6x-20)

A: Consider

Q: y'sec²xdx – (1– 2y'tanx)dy = 0

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Q: Find the product or quotient of pair of complex numbers. A. 4(cos 40° + i sin 40°) •5(cos 70° + i…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: x(8x*-30x +5x-80) 14. S(x* – 3x³ + [? -2)dx | 40

A: Given : Let the missing value be A∫x4-3x3+A-2dx=x8x4-30x30+5x-8040+C   To Find : The value of A

Q: Solve for x in terms of a and b. log x = - 10(log a + log b) + 8 log b° + 5(log b – log a) = x Write…

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Q: Find the particular solution determined by the initial condition. f'(x) = 3x2/3 - 4x3; f(1) = - 8…

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Q: Maximize and minimize f(x, y, z) 3x + y + 2z subject to 2x + 3y2 + 4z² 210 %3D

A: We have to use lagrange multipliers.

Q: 4. Find the inverse, domain and range of the function f (x) = x +3

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Q: Determine whether the lines Lj and L2 are parallel. L1: x = 3 – 4t, y = 5 + t, z = 8 – t L2: x = 5 –…

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

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Q: Find parametric equations of the line through (-3,0, 4) that is parallel to 5i– 8j+k. x(t) y(t) =…

A: Parametric equations of a line passing through the point P(a,b,c) and parallel to the vector v→=…

Q: 2. y = x2, y = x³ , revolved at y axis

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Q: 2(n!)2 (2n)! n=1

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Q: dx =+c 6. 2.

A: We can solve the given problem as follows:

Q: af when r = 2, t =- 1 of the function ar 4. Use the Chain Rule to find- f(x, y, z) = e3xy² cos 2xyz…

A: This is a problem related to chain rule for differentiation. Based on the formula we will find out…

Q: Using Lagrange multipliers, find three positive numbers whose sum is 24 and such that the sum of…

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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 an equation of the plane that passes through the point P(-7,-2,5) and has the vector n = (-7,4,…

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Q: (a) Express the vector field D = (x² +y<)-1 (xax – yay) in cylindrical components and cylindrical…

A: To express the vector field  in cylindrical components and cylindrical variable.

Q: Consider the points A(1, –1,4), B(2, –3,2), C(-1, –2, 2), and D(4, 3, –6). (a) Find the volume of…

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Q: 2y Find the directional derivative of f(x, y, z) = x + z at P(4,4, –3) in the direction from P to…

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