Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) 3x² 3xy + xyz (a) Find the rate of change of the potential at P(2, 6, 5) in the direction of the vector v = i + j - k. = (b) In which direction does V change most rapidly at P? (c) What is the maximum rate of change at P?

Q: Q3/ A. For the following function f(x). Find: i. iii. f(x) = x² + 1 The slope of the f(x) by using…

A: We need to find out the slope using the definition.

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A: Given: y''-2y'-15y=0, y(0)=α, y'(0)=-9

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Q: Q4: (chose one only) 3-x 1- f(x) = 2 x 2 a) Find limx→2+ f(x), limx→2- f(x) andf(2). b) Dose limx-2…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x - sin²x

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A: Given: v(t)=10 -t, 0≤t≤5.5

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 2 (1) limx-o[: 1-cos x sin²x (2)…

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A: Since you have posted multipart questions i can do first three subparts as per our company…

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Q: Q5: Find for the following functions: dy dx (1) In(x - y) = xy + y² ;

A: Find the derivative

Q: 2-) -100

A: Since you are asking multiple questions. We are answering only one question as per our guidelines.…

Q: Q4: Answer two only: 4 2 2 1 -1 1 (A): If A = -2 Find AB and AC. 01 0; 2 B = 2 -1 3 -2 -2 and 2 1 3…

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Q: Q2: Solve the following integrals: (1) 7x²+14x+15 (x²+3)(x+7) dx ; (2) sinx+cos x sin³ x cos³ x

A: Since multiple questions are asked, I am answering first question

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A: Need to find out the Wy1,y24

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A: Our Aim is to evaluate the integral given below:-∫sin θcos θcos2 θ-9dθ -(i)

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Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x sin²x (2) lim, o…

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Q: doesn't this mean there are no critical points

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A: The function f(x)=x2+3x from x1=2 to x2=4

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Q: Q1: Fill in the blanks for the following statements (chose five only) 4n 1. lim-00 2n+1 2. log10 (3x…

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Q: (B): Find the tangent equation to the curve y = sin² x at point x = 7.

A: I have stated the used formulas in the solution

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Q: Solve the initial value problem 25y" - 40y' + 16y = 0, y(0) = 2, y'(0) = 3. y(t) = How does the…

A: We have to solve the initial value problem 25y'' - 40y' + 16y = 0 y(0) = 2 & y'(0) = 3

Q: Precalculus Let cos0 = 5/13, 3π/2 < 0 < 27. Find the exact value of each of the remaining…

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

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Q: Q2: Solve the following f (1) 7x² +14+15 (x²+3)(x+7) dx :

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