Find the gradient of the function at the given point. Function Point f(x, y, z) = V x? + y? + z? (5, 2, 8) V(5, 2, 8) = Find the maximum value of the directional derivative at the given point.

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(3, 2...

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Q: In Exercises 1-4, use the comparison test to confirm the statement. 1. 2 diverges, so diverges. n-3 ...

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Q: Obtain the solution using Integrating Factors Found by Formulas. 1. 2(2y2 + 5xy – 2y + 4)dx + x(2x +...

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions specify...

Q: dations. 1. sinx siny dx + cosx cosy dy = 0

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Q: 2. What is the slope of the normal line to the curve 4x2 - 9y2 = 1 at point (3,2) ? a. 3 b. - 8. С. ...

A: Normal at any point on the curve is a straight line that intersects the curve at that point and is p...

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

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Q: Find the directiona f(x, y) = x³ – y³, P(4, 3), v = (i + j)

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Q: Voter Registration The amount of voters in a city's district should grow at the rate of R(t) = 150...

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Q: Let X be a random variable with p.d.f f(x) = 2x,0 < x < 1. Find E(Vx). 2/3 5/4 3/2 4/5

A: Given

Q: Determine the homogeneity of the following function x^3-xy+y^3

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Q: (1-x²)-1/2 Arcsin x

A: We will integrate the given function using simple Integration method.

Q: ind any critical numbers for the function f(x) = 6x - 3x +8 and then use the second derivative test ...

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Q: Exact equations: Solve * (2x + 3y) dx + (3x + y - 1) dy = 0 O x* + 6xy + y² – 2y = c O y2 + y* = c

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Q: 13.Exact equations: Solve: (2r3 + 3y) dx + (3x + y – 1) dy = 0 O x* + 6xy + y² – 2y = c O r?y² + y* ...

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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) F(t) = 4t3 %3D L{f(t)} %3...

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Q: 4 5 y = x? – 8x – 6 + - 8x – 6 +a

A: We have to differentiate the given equation. 

Q: Find the gradient of the function at the given point. g(x, y) = 18xe"/x, (3, 0) Vg(3, 0) =

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Q: Find the coefficient a of the term in the expansion of the binomial. Binomial Term (6x-y)^12 ax^4y^8

A: The given binomial 6x-y12

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

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Q: Consider the parallelepiped with adjacent edges u = 5i + 7j + k v = i+j+2k w = i+ 9j + 2k Find the v...

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Q: Which of the following sets of vectors in RS are linearly dependent? Note. Mark all your choices. O ...

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Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer alge...

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Q: r = sec(20)tan(28)

A: To find the derivative of the function.

Q: find the integration of 1/(sinx*√(sin(2x))) .dx

A: Let's find. 

Q: Graph the function f(x) = x+4/x Graph the secant line that passes through the points (1,5) and (8,8....

A: To graph the function fx=x+4x.To graph the secant line that passes through the points 1, 5 and 8, 8....

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

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Q: the

A: We will find the vertical asymptotes if it exists. 

Q: By applying Rolle's theorem, check whether it is possible that the function f(x) = a° + x – 6 has tw...

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Q: 6. (Sections 8.8 and 8.9) Determine whether the following piecewise-defined function is a probabilit...

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Q: 2. Find the general solution of the differential equation: dy ip 5 + 6y = e ,3x - dx? d.x

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Q: cotx dx In|csc x| cSC

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Q: 24. Vnt +1 n³ + n n=1

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Q: Q1: Find the solution of the following Differential Equations 2. dx + 3y = e* + 2 3. dx2 x = 0 dx

A: We will find the Differential equation solution 

Q: iven the points A (-7, -2), B (5, -2), and C (0, 8), determine the area of the shape ABC. The area o...

A: Given problem:- Given the points A (-7, -2), B (5,-2), and C (0, 8), determine the area of the shape...

Q: e dx

A: Definite integration

Q: 38. At what value of x should the function f(x) = In(x – 4) approach to so that f(x) will be as smal...

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Q: A function f(x) and interval [a, b] are given. Check if Rolle's Theorem can be applied to f on [a, b...

A: To test whether Rolle's theorem is applicable or not.

Q: = xe 10) Determine the absolute maximum and minimum for f(x) on the interval [0, 3].

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Q: s3 + 3s2 – 12s + 4 e) lim s-2 s3 - 4s x- V3x + 4 f) lim x4 4 - x x² + 4 – 2 g) lim

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Q: 16. Find the area of the shaded region. Leave your answer in terms of pi. 50'

A: The solution is given in the next step.

Q: 1. Find the general solution of these constant coefficient linear inhomoge- neous ODES, using the me...

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Q: TE: Enter the exact answers in terms of i,j and k. Same direction as – 3i + 5j. u = Oppositely direc...

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Q: For each of the following rational functions, determine where the vertical asymptote(s) of the funct...

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Q: Separation of Variables: Solve for xy dx + (y + 1) e*dy = 0 O xe – e - y - 2y² = c O xe - e -- = C 2...

A: The given DE is: xy3dx+(y+1)e-xdy=0...(1)

Q: Q1: Find the solution of the following Differential Equations d²y 1. + y = 6e* + 6 cos(x) dx2 d?y 2....

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Q: 1. Let f (x) = x (cos(2a)+ sin(3x)). a. Find the average value of f (x) for 0 <x < T. Show your work...

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Q: Evaluate. S*+ 2y)dx dy 3.

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Q: Solve for all vectors X so that × X = .

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Q: 36,37

A: As per our guideline is multiple questions are posted we are supposed to answer only the first one. ...

Q: S sin(V2x)dx = sin(V2x) – V2x cos(v2x) + c %3D

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