Find the gradient of the function at the given point. In(x2 – y) – 9, (3, 8) z = Vz(3, 8) =

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Q: Compute the length of the curve r(t) (-6t, 4t + 4, –5t – 3) over the interval 0 <t < 7. (Use…

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Q: 4. Let f(x) be a function that satisfies f(3x) dx = 1 and 3f(x) dx = 15. Calculate f(x) dx. Show all…

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Q: 6. Differentiate y with respect to x using A-method. x-3 a. y = X b. у %3D V4x + 3

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

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Q: Let R and S be the relations defined as below 2. R = {(1,2), (1,3), (2,3), (2,4), (3,1), (4,1)} S =…

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Q: Solve the initial value problem. - + 4y = 7, y(0) = 1 dt The solution is y = O

A: Given query is to find the solution of the differential equation.

Q: Use the First Derivative Test to find the location of all local extrema for the function given…

A: The given function,    f(x)=-7+20x2+10x33

Q: 2. Evaluate the following limits. cos X h. lim-

A: Limit

Q: Determine if the following statement is true or false. The points P,(2, 0, 1), P2(3, – 2, – 3),…

A: We know that three points P1, P2, P3 lie on the same line if direction ratios of P1P2 and P2P3 are…

Q: 4. dx + (x – y + 2)?dy = 0

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Q: f(x, y) = 2y – 6ry - x 2.

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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: 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: Find the directional derivative of f at the point P in the direction of a. i-j f (x, y) = 2x3 – 6y³;…

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Q: y 71. f(x, y) y %3D

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Q: af Find a d () + In (). of the function f(x,y) = arccot and ду

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Q: Determine the sum of the following series. 1" + 6" 8n п-1

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y² + z² (5,…

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Q: Maximize f(x, y) = 3xy Зху subject to x + y = 1

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Q: x2 1. Let f(x) = 3Vx² – 1 and g(x) = x4 81 (a) Determine the domain of f and g. (b) Compute gof and…

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Q: -3/2 dx S(35 + 4x – 4x²)

A: Explained below

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: 1 Using u = 1 + 2x6, then the integral | x°(1+ 2x6)5 dx becomes 12 us du- This evaluates as 5+1 1 12…

A: Follow next step

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (3, –4)…

A: A detailed solution is given below

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 an equation of the plane that is parallel to the plane x + 7y – 2z + 20 = 0 and contains the…

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

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Q: Solve the Bernoulli equation. -6 5xy' +y = y°, x>0

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

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Q: Determine if the following statement is true or false. The points P1(12, 8, 9), P2(6, 2, 0), P3(0, –…

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Q: r = 3 cos 0

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Q: then the distance from a point P to the line L is equal to the length he component of the vector AP…

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Q: Two angles are supplementary. If 2 times the measure of one angle is 6 times the measure of  the…

A: This question is based on that supplementary angles sum equals 180 degree.

Q: Evaluate the integral. S(-241 - s)at 3 xdx = 2 15 given, a'dr = x²dx = dx = 1, O -36 O -146 O -114 0…

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Q: ne indicated function y, (x) is a solution of the given differential equation. Use reduction of…

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Q: Determine if the following statement is true or false. The points P1(14, 8, 9), P2(7, 2, 0), P3(0, –…

A: Find your answer below

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: Find two unit vectors in 2-space that make an angle of 45° with 7i+6j. NOTE: Enter the exact answers…

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Q: Given that Vf(12, – 7) = 9i – 4j, find the directional derivative of the function f at the point…

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Q: Using Jacobi Method solve the following system: 2х1 — 6х2 — Хз — —38 -3x1 - x2 + 7x3 = 34 -8x1 + x2…

A: Given that the system of equations are 2x1-6x2-x3=-38-3x1-x2+7x3=34-8x1+x2-2x3=20. First check…

Q: Question Use the First Derivative Test to find the location of all local extrema for the function…

A: Given problem:- Use the First Derivative Test to find the location of all local extrema for the…

Q: Find the vector component of v = 2i – j+ 3k along b = i + 4j + 8k and the vector component of v…

A: Vector

Q: For numbers 4-10, answer the following questions for the piecewise defined function f(t). t2 t+6 for…

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Q: 25x at P(5,0) in the x + y Find the directional derivative of f(x, y) direction of Q(2, –2). NOTE:…

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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

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

A: Let's find.

Q: Evaluate using Integration by Parts. (Use symbolic notation and fractions where needed.) xeSx+6 dx…

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