39+ 5 dy (5y~7)2

Q: [2x/4 +x? dx

A: Here we have to integrate the given problem.

Q: at aw (b) Find at using partial differentiation of the function f(r, s, t, w) from the given…

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Q: Use Lagrange multipliers to find a vector in 3-space whose length is 6/3 and whose components have…

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Q: If F(u,v) = (u-v) / (u+v), Find r(금금)+ F(x)

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Q: 3. Let u =x² – 2xy+2y' with x = s´ · Int and y = 2s ·t° . au au and at Find as

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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, Р(5,…

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Q: The Acme Widget Company has found that if widgets are priced at $125, then 2700 will be sold each…

A: It is given that Acme Widget Company has found that if widgets are priced at $125, then 2700 will be…

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: n(n + 1)(2n + 1) 3. Le n be a positive integer. Use induction to prove || 6 j=1

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Q: Question 1 Given: xy = tan(a - y). Find dx/dy. %3D tan (z-y) sec (r-y)- " +tan? (-y) sec" (7-y) O dr…

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 6j as…

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Q: Q2: What is the value of second derivative of f(x)=3 sin((1-x)/t) *

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Q: The first step in solving the integral of tan(x)dx/[1-(tanx)^2] is by transforming the tan(x) O In…

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Q: X Your answer is incorrect. Edit Find the vectors that satisfy the stated conditions. NOTE: Enter…

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Q: Determine whether the series converges. 1 k + 11 k=I The series

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Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 2+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are…

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Q: Reindex the series to start at k = 0 y = E, (k+ 1)æ*+3 = E£o

A: The given series is y=∑k=7∞k+1xk+3 we have to re index the series to start at k=0. Rewrite the given…

Q: Integrate the following differential and determine the constant of integration: dy/dx = 8/x which…

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Q: 1. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of…

A: The Lagrange multipliers method is a strategy for finding local maxima or minima of a function using…

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

A: Given that the function is fx=x3-4x2x+22 its first derivative and second derivative is…

Q: Find the directional derivative of f at P in the direction of a. f (x, y, z) = xy + z²; P(3,4,–4); a…

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Q: Consider the IVP: x" + 3x' +2x = 4t2 ; x(0) = 0, x'(0) = 0.

A: Given,  x''+3x'+2x=4t2, x(0)=x'(0)=0

Q: a 19.) sin u f&) dx where f) = Co x4 /2 Sxい円

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Q: 6dz SVE -)dt

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Q: Find the area of the triangle with vertices P(1, 3, –3), Q(0,0, 0) and R(4, 5, 1). NOTE: Enter the…

A: Here, PQ=Q-P=0,0,0-1,3,-3=-1,-3,3PR=R-P=4,5,1-1,3,-3=3,2,4

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges.…

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Q: Find Duf at P. 2. f(x, y, z) = 4x³y°z²; P(1, –2, 1); u = i+ Duf = i

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Q: Now, let f"(x) =0 and solve for x. Remember that f"(x) = - sin is a periodic function, and thus…

A: use the equation above for solving the equation for x.

Q: 2. If f(x)=x² – 5x find, a. f(y? + 1) b. f(z+1)-f(z-1)

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Q: et +2e2t-et dt e2t +1 6.

A: Follow the procedure given below.

Q: Approximate the critical numbers of the function on the open interval shown in at each critical…

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Q: Find all values of x in the interval [0, 27] that satisfy the equation. (Enter your answers as a…

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Q: Use OP at the right to find the length of DB. s0 6 cm The length of DB iscm. (Simplify your answer.…

A: Let's find.

Q: dx 21 + C %3D

A: We have to find the value of ?

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 the…

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Q: Write the scalar equation of the plane with normal vector - [1, 2, 1) and passing through the point…

A: We know that equation of plane passing throgh the point (x1,y1,z1) and perpendicular to the vector…

Q: Find a formula for f'(x) and determine the slopef'(-5) for the following function. 6e f(x) - Te* + 6…

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Q: The evaluation of So So x y e**dxdy is 0.5 e 0.25 e - 0.5 O e - 0.25

A: Double integral

Q: sin4x S V cos4x + 1 dx

A:

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

A: use partial derivative for finding the gradient.

Q: Match the graph of f, below, with that of its derivative. 3. -3 -2 -1 I 2 3 -3+ 4 ++ -6 -4 -2 4 6 2.…

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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…

A: Solution is here

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

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

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

A:

Q: 4x – 6 2. Let f(x) 1– (2x – 3)3 a. Find the Taylor series representation for f about x = 1.5 that is…

A: Let's find.

Q: (-1)" Given: In(1+ x) = > if |a| < 1. n + 1 n=0 3. Use the third degree Maclaurin polynomial of f to…

A: We can solve this as follows:

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

A: The given function whose maxima or minima are to evaluate is: f(x,y)=xy with the constrain…

Q: 3. -2 -5 Find the va lue of Hif Xi+xdx 3.

A: 3-2-518H-134=∫03x1+x2dxPut 1+x2=yas x →0 ,y→1as x →3 ,y→2differentiate on both…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = x² + y2 + z* (5,…

A: To find gradient of the function at the given point.