3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x– y + z = 2 and x + y – 8z = 4.

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Q: 10. Maximize f(x, y) = 25 – ² - y² subject to 2x + y = 10

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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: 4. dy – (x - y + 1)²dx = 0

A: As we know that; ∫dxa2-x2=12alnx+ax-a+C   The given differential equation is: dy-x-y+12dx=0 So, we…

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Q: Given: a1 = 4, d= 10 Answer the following questions. Part: 0 / 2 Part 1 of 2 (a) Write the first…

A: A detailed solution is given below.

Q: Exercise I f(1, y)yz (a) Let f(r,y) = rỷ - . Then deduce that f(1,y)zy (Clairaut's theorem). %3D

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Q: sin 2x cos 2X I+ 3 cos4X

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Q: 20x at P(4,0) in the x + y Find the directional derivative of f(x,y) direction of Q(2, –1). NOTE:…

A: The expression for the directional derivative of the function f in the direction of u is:…

Q: 2. Let g(x) = ev cos +, Approximate the value of g(0.2) using the second degree Maclaurin polynomial…

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Q: 2. f(x) = x² - 5x + 6 A. x = 1 B. x = -3

A: This is a problem related to limit and continuity parts of the calculus. Based on the general…

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Q: * (Find the integral of e^2x c

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Q: 2. Evaluate the following limits. x²-6x+9 b. lim X-3 x-3

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Q: Find an equation of the plane through (-2, 8, – 5) that is perpendicular to the planes 2x – y + z =…

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

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Q: 6. Find the volume of the solid obtained by rotating the region bounded by the given curves about…

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Q: Use the Chain Rule to find- af when r = 2, t =-1 of the function ar f(x, y, z) = e3xyz cos 2xyz ; x…

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

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of PQ.…

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

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Q: 7. Х Arcsec (2х) dx 3 (4x2 – 1)7

A: The objective of the question is evaluate the indefinite integral.

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

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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: 28. f,(2,4) if f(x, y) = x* In y

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Q: 4. dx + (x – y + 2)²dy = 0

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Q: Verify that the Mean Value Theorem (MVT) applies to the function f(x) = sin' 37 and find all the…

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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 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 Comparison Test to determine if the series converges or diverges. Sn + n=1 diverges…

A: Solution: ∑n=1∞55n+6n Apply constant multiplication rule : ∑c·an =c·∑ an =5·∑n=1∞15n+6n

Q: 1. Given: - 4r? with f'(r) = (r+ 2)2" r(r+8)(r – 2) (x+2)3 8(7r-4) (x+2)4 f(r) = and f"(x) = %3D %3D…

A: fx = x3-4x2x+22 ; f'x = xx+8x-2x+23; f''x = 87x-4x+24

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Q: Using algebraic substitution, differentiate the following |2+ Vx dx

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Q: To test this series for convergence 4" - 1 1 You could use the Limit Comparison Test, comparing it…

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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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