D O 1.909 Question 14 Find the length of the plane curve given below. r(t) = 5cos(t)i+5 sin(t)j, [0, 4] 09 O 21 O 20 O 19 O 25 Question 15 Find the curvature K of the curve given below.

Q: Consider the following. (Round your answers to four decimal places.) f(x, y) = x cos(y) (a) Find…

A: Solution of given question is written in below steps.

Q: At how many points do the curves r₁(t) = ((t + 1)², — t² − 2t, t+2) and r₂(t) = (1 – t², t, t) -…

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Q: 4. The process of finding a general formula for the slope of a line tangent to a certain curve is…

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Q: Find the critical points of the given function. a) f(x) = √2²-4 b) f(x) = 3x + 21-1

A: To find the critical points of the given functions.

Q: In a classic video game, balloons travel from left to right along a linear path that passes through…

A: Given equation is :   x-12+y2= 100 ---- equation of circley=3x+7 --------equation of line

Q: V. Provide up to the 5th degree Taylor Polynomial of the given function: f(x)= xex by about x=-1

A: Given :fx=xe-xx=-1

Q: Show your complete solution: Evaluate the triple integral ㅠ pxy 2 L x 0 COS Zdzdydx X

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or sin(8n) Σ 47 n =…

A: We will use Ratio-Test to find convergence

Q: Rewrite the following equation with the variables separated. 3xy' + 2y = sin(y). dy (sin(y)+2y) O O…

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Q: (2) Use a known Maclaurin series to obtain the Maclaurin series for f(x) = sin²x. (Hint: Use sin²…

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Q: Find the average value of f over the region D. f(x, y) = 6x sin(y), D is enclosed by the curves y =…

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Q: identify the following quadric surface x^2/6 + y^2/6 + z^2/16 =1

A: This question is related to Quadric surfaces, we will solve it using given information.

Q: y' = 2xy²

A: Given: y'=2xy2We need to solve the above differential equation.

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

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Q: Find the second partial derivative for the function z = x7-7xy + 6y2 with respect to x.

A: Solution of given question is written in below steps.

Q: Given that S." sin xdx = 2, find the average value of the sine function on the interval [0, π].…

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Q: -1 xp(x + 1)zz² J

A: The given integral,        ∫-11e2x1+xdx

Q: 3. Suppose [ f(2)dx = 36, So r)dr the following: a. b. f f(x)dr 50 f(r)dr = 12, (2ƒ(r) + +12g(r) -…

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Q: Match the graph of the surface with one of the contour maps. f(x, y) = e¹-x² + y²

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Q: Prove the identity. 1 + sin x 1- sin x = (secx + tan x)² To verify the identity, work each side…

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Q: Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the…

A: Here, the given parametric equation is: x=1-t2, y=2t-t2, -1≤t≤2

Q: parametric

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Q: Use logarithmic differentiation to find the derivative of y y = X X+7 OA. OB. O C. (3)√ 2 7 O D. X…

A: topic- differentiation properties of log used:log(ab)=blog(a)logab=log(a)-log(b)derivative formula…

Q: Find the volume when the following region is rotated about the y-axis: y = √4x², y = 0, x = 0.

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Q: Find the general indefinite integral. (Use C for the constant of integration.)

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Q: Evaluate fx and fy at the given point. f(x, y) = e¹³y sin(x), (π, 0) fx(π, 0) = (No Response) fy(π,…

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Q: multiple of a and c: =b/(n^3) c = b/(1 + n^2) S 1 du au²+bu+c

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Q: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not…

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Q: Given the function xye9-sin² ecos² fxx of f is equal to 0. f(x, y)= The second derivative Select…

A: A detailed solution is given below. fx = partial derivative of f(x,y) with respect to x. fxx =…

Q: + 2 .4 i ti ti ti ti + i _ ។ { / - 1 "

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Q: find an equation in rectangular coordinates for the equation given in cylindrical coordinates r= 2z

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Q: Consider the following functions. f₁(x) = x, f₂(x) = x², f3(x) = 7x - 3x² g(x) = c₁f₁(x) + C₂²₂(x) +…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: 1. y = x-3 2x³+x²-18x-9

A: As per our guidelines we are supposedly to  only one question. Kindly repost others question as a…

Q: Calculate the sum of the series Σ n = 5-6(0.6)" 00 n = 1 n whose partial sums are given.

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Q: Evaluate sin'0 cos de Ꮎ

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Q: Solve the initial value problem: y(x) = 0. dy da + 3y = 7, y(0) = 0

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Q: 2. Use integration by parts to solve for [x³c x³ cosx dx.

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Q: ΒΣ 3 Θέλη

A: 3.The given series ∑n=0∞3.12n

Q: Find the average value gave of the function g on the given interval. 9 ave 11 g(t) = t √8+2² 8 + t…

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Q: Find the total differential. w = e²y cos(7x) + z³ dw = (No Response)

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Q: a) 2+ + = 1. H

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

Q: Determine the area between the graphs of the equations y=x and y=(x)^2-1. Integrate over the x-axis…

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Q: Utilice la regla del producto para derivar y = (2x² + 2x + 1) (3x - 4) Llene los blancos (sombreados…

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Q: 1. f√√x²dx 2. Jdx 3. (2x + 3)² dx (4x²–5x+6) 4. S x² 3 5. f ( t + 1)²³ dt S dx

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Q: The figure to the right shows four regions bounded by the graph of y=xsin x: R₁, R₂, R3, and R4,…

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Q: Find the critical points of the given function. 1 a) f(x) = -√24/3+2¹/ +2-2/3

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

Q: Use a sum or difference identity to find the exact value of the expression. 7π 12 sin

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Q: (c) State the Fundamental Theorem of Calculus Part II.

A: In this question we have to state the Fundamental Theorem of Calculus Part II.

Q: 52. If lim f(x) = 6 and lim, g(x) = 3, find x-2 (a) lim [5 f(x) - 4g (x)] (b) (c) lim [4 - xf(x)]…

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