Represent the plane curve by a vector-valued function

Q: y 3 y = V x 1 (1, 1) X = 8 y = X 2 4 6 8

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Q: Compute each sum below. If applicable, write your answer as a fraction. 4 + ...+ 4(3)- 0 + 4(3) +…

A: Use geometric series sum concept

Q: find in Verse, then domain t range 8-X\ = (x)} OD:[8,8),R:[O,00) 2 All Real Numbers 8.00

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Q: (c) f''(x) = cos x, f(0) = 1, f'(0) = 2, f"(0) = 3.

A: Explained below

Q: Determine the equation of the tangent to the graph of the equation xy – 2x'y-3ry + 5y – 4 = 0 at the…

A: To find the equation of tangent to the given equation at (1,2).

Q: o<×くT ② Foのコ 2 [:

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Q: +4

A: To check the convergence of the given improper integral:∫-∞2dxx2+4

Q: Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the…

A: We need to set up and evaluate integral.

Q: Find the directional derivative of f(r,y, z) = e² cos(Tyz) at (0, 1, ) in 2-1 -y-1= I-2 the…

A: To Find: Directional derivative

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: For each of the following series determine if the series converges or diverges. 00 In(n) Σ n n=2 n3…

A: The given series,1. ∑n=2∞ln(n)n2. ∑n=0∞n3n4+1

Q: x – 1 - V3x +1 lim Зх + 1 x→5 X – 5

A: Solution:

Q: ind lim f(x) for the given piecewise function. x-4 2х + 5 if x 4 E the limit does not exist, enter…

A: Topic  = Limits

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 7 cos(t)i + 3 sin(t)j+…

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Q: S%3200000 e° find the growth rate of S.

A: Given query is to find the growth rate.

Q: Find the derivative of this function

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Q: Find V· (F × G), if F(x, y, z) = 8xi+j+8yk and G(x, y, z) = xi+ yj – zk. V · (F × G)

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Q: Consider the functions. f(u) = u³ + u g(x) = cos (x) Find the following function and derivatives.…

A: The given functions,fu=u8+ug(x)=cos(x)

Q: Solve the equation for x and y x+v=300 5x+8y=2100

A: Given query is to find the solution of the system of equations

Q: Consider the matrixes 0 3 -9 k A = O .B = ( , 7 7 62 k is a real constant M = (A-B-1)-1 If m22 = 14…

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Q: 5 Sine cose do 1. Sine+ 3sine - 4

A: Indefinite integral

Q: Find V x (V × F) if F(x, y, z) = 8xyj+7xyz k. V × (V × F) =

A:

Q: Hello, complete the attached Calculus question correctly and show all your work. Please use the…

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Q: Find V · (F × G), if F(x, y, z) = 2xi+j+14yk and G(x, y, z) = xi + yj – zk. | V · (F x G) =

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Q: ||r(t) × r"(t)|| ||r'(t)||* Use the formula k(t) : to find k(t). r(t) = e"i+ ej K(t) :

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Q: In(1+x) -x cosx -1 1. lim x-+0 7- In(2x + 3) 3. lim x-00 In(5x -2)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 24x from (24, 24) to (0,0). NOTE:…

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Q: The graph of the first derivative f' of a function f is shown. (Assume the function is defined only…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 31.| CSC I COLI dt

A: We will use substitution method to solve both the integral.

Q: Find the 4** x³ dx А. + c 4 In 4 В. + c 4 In 4 С. + c 3 In 3 D. 24 2 In 2

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Q: 86. If f'(x) > 0 for all real numbers x and s(1) đt = 0, which of the following could be a table of…

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Q: Consider the piecewise-defined function Jr+3, |1- x, x 0. (a) FUNCTION, so it must pass the…

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Q: sin(x) 19. Evaluate -dxdy by changing the limits of integration appropriately.

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Q: Find dy/de y=(1 +Sin 94)6

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Q: 14th term of the following geomnetric sequence. Find the 1. 2, 4, 8, 0. 昌 唱

A: Use geometric series concept

Q: Describe the graph of the equation. r = 4 cos t i – 14 sin t j + k O An ellipse in the plane z = 1,…

A: Here, the given parametric equation is: r=4 cos t i-14 sin t j+k⇒r(x(t),y(t),z(t))=(4cos t, -14 sin…

Q: 7. -4 3. ) -3 7. 1) 10. 2)

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Q: mparison test to determine whether the given series conve:

A: Please refer to the image below

Q: 5² - 13 ニ

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Q: 1. Do the integration by substitution for the following integral and find the value of definite…

A: We have to find the given integral value.

Q: Find V · (V × F) if F(x, y, z) = 10 sin xi + 5 cos(8x – 9y)j+ 4zk. V· (V × F)

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Q: Find the J(2x + 1)³ dx

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Q: 4 fy 1 -3 -2 1 -1 -2

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Q: Evaluate the integral. (Use C for the constant of integration.) 2 cos (a) da sin(a)

A: Given query is to find the value of the integral.

Q: 55-58 Use the properties of integrals to verify the inequality without evaluating the integrals. 55.…

A: Let's find.

Q: In(v¤) dædy 6. 15. Calculate ry

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Q: Find curl (5z i + 6x j + 3y k). curl (5z i + 6x j + 3y k) = ( i )i + ( i i )k

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Q: Evaluate the limit: r(t + h) – r(t) lim h >0 for r(t) = (t°, sint, 1) h r'(t) = (

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Q: Evaluate the given integral by changing to polar coordinates.     sin(x2 + y2) dA   R, where R is…

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Q: 7. -4 3. ) dx - 3 10.

A: The given integral,         ∫e5xe2x7+3e3xdx