Find the arc length L of the graph of r(t). r(t) = 2 cos(t)i + 2 sin(t)j + tk, 0≤ t ≤ 2π

Q: Find the Maclaurin series and corresponding interval of convergence of the following function. f(x)…

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Q: Find dy/dx by implicit differentiation. (sin mx + cos my)4 = 74 dy/dx=

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Q: Find the derivative of the function by the limit process. g(t) = t³ +7t g'(t) =

A: We have to find derivative

Q: Find the exact value of cos(195°) using the fact that 195⁰ = cos(195⁰) = 225° -30°.

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Q: Find the interval of convergence of n²x³n 33n n=1 interval of convergence = (Enter your answer as an…

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Q: Find all points of intersection of the given curves. (Assume 0 ≤ 0 ≤ 7. Order your answers from…

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Q: Which of the following is the derivative of (x³ + 1)(x² + 2x)? 3x²(x² + 2x) + (x³ + 1)(2x + 2) 3x²…

A: This question is based on product rule of differentiation.

Q: Find the volume of the solid obtained by rotating the region under the graph of the function f(x)…

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Q: For the given vectors a and b, find the cross product a × b. a = (1, 0, -3), b =(3, 4, 0) axb=

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Q: 1. F = cos y i+ xyj + yk, A B C D E F О н A. i+j+(y-siny)k B. i+ (siny - y)k C. j (2y-siny)k D. 3i -…

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Q: Find all solutions of the equation in the interval [0, 27). 2cos’x– cosx−1=0 Write your answer in…

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Q: 12. Prove that the intersection of any family of normal subgroups of a group (G, *) is again normal…

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Q: Activity 2.2 For the given function sketch the graph; determine if f is continuous at xo and…

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

Q: ☎ Q1: If x=² and y=21³ then b) 3 314 ² dx d) at x=4 F others Choose

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Q: Use Green's Theorem to evaluate the line integral √(x - (y - x)dx + (2x - y)dy for the given path.…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 9x2/3 dy = Need Help? Read It…

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Q: 10. Given that y = at x = 1. e* X + 1 Find, in terms of e, the values of . 최 and dx dx²

A: (10). Given: y=exx+1   As we know that; The Power law; ddxxn=nxn-1 The Quotient rule;…

Q: 1) fx-²dx 2) sin(n)dx

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Q: Evaluate the triple integral zdV where E is the solid bounded by the cylinder y² + z² = 64 and the…

A: Here, to evaluate: ∫∫∫Ez dV where E is the solid bounded by the cylinder y2+z2=64 and the planes…

Q: Find The complete Solution of the differential eqution y" +24+4y=cosx Subjected to The condition…

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Q: III. Find a set of equations of the line passing through (4,2,-1) and parallel to the line of…

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Q: Find curl F and div F given F(x, y, z) = e* siny i+ esinzj+e-² sin x k

A: Given  Fx, y, z = e-x sin y i + e-y sin z j + e-z sin x k We have to find curl F and div F.

Q: Find T5(x): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a = 0. T5(x) = = Using…

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Q: Find the volume of the ellipsoid x² + y² + 10z² = 49.

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Q: [2,

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Q: 5 If [F(x) dx f(x) dx = 7.4 and 1.°F(x) dx f(x) dx = 5.7, find [²1 f(x) dx.

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Q: 5. Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (1, 0, 0) to…

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Q: What are the rectangular coordinates of the point whose spherical coordinates are (1, ½π, π) ? x = Y…

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Q: y = x² + 2 Δy = dy= Need Help? x = -3 Read It Ax dx = 0.01 Watch It (Round your answers to four…

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Q: 3- For what value of c is the function continuous? Provide a well- communicated solution. F(x) = {…

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Q: d the area inside ²4 sin 20, 8 4 16 0≤0≤

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Q: For F(x, y, z) = y²z³ i + 2xyz³ j + 3xy²z² k, determine whether or not the vector If it is…

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Q: Solve for the solution of: (D2 - 4)y = 8e2x - 12

A: Given problem:- Solve for the solution of: (D2 - 4)y = 8e2x - 12

Q: Consider the series (4x)n n n=1 Find the interval of convergence of this power series by first using…

A: Given problem:-

Q: 6. Use Green's Theorem to find the counterclockwise circulation and the outward flux for the field F…

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Q: Find the exact length of the curve. X = v 3 y (y - 3), 16 ≤ y ≤ 25

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Q: Evaluate (F JC Er F • dr. F(x, y) = xi + yj C: r(t) = (7t + 4)i + tj, 0≤t≤1

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Q: 6- Write four examples about sketch the graph in polar coordinates from families of cardiod and…

A: Let's find.

Q: 17. Let y = 4t² + 3, t = 6es and s = 1 + In x. Find in terms of x. dx 18. Given y = 5t (3 - t), t =…

A: Let's find.

Q: Find DO NOT SIMPLIFY YOUR ANSWERS. 1. log √2x² + y + 2x² + y) + tan(x™ — ñ³) = sin¯^¹²(x² − 1) + ½ /

A: To dydx.log32x23+y+tanxπ-πy=sin-1x2-1+π2

Q: Activity 1.3. B Evaluate the limits of the following functions. 3. lim (ex + 2) -X+0

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Q: Express the limit as a definite integral on the given interval. n lim [7(x)³ - 5x;*]4x, [2,7] n→∞ =…

A: Here, the limit of the integral is [2, 7]. Further, ∆x is replaced by dx and replace xi* by x. Thus,…

Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = e, y = 1…

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Q: SCALCET9 11.5.006. Test the series for convergence or divergence using the Alternating Series Test.…

A: Use alternating series test to check the convergence of series

Q: Solve xy = 8y - 3x, y(1) = −1. (a) Identify the integrating factor, a(x). a(x) = (b) Find the…

A: xy'=8y-3x

Q: Find . DO NOT SIMPLIFY YOUR ANSWERS. 1. log₂ √√2x² 2x² + y) + tan(x² − π²) = sin¯`¹²(x² − 1) + ½ /

A: To find dydx.log32x23+y+tanxπ-πy=sin-1x2-1+π2

Q: use the constrained variation to maximize the volume of an open cone when the surface area is 2π

A: use the constrained variation to maximize the volume of an open cone when the surface area is 2π

Q: Suppose you deposit $1000 at 7% interest compounded continuously. Find the average value of your…

A: To find out the average value of account during first 4 years.

Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 3 P3(x) =

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Q: The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the…

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