(1–3)* (t³ -8) t + 2 4. 2-t

Q: Determine whether the following series converges or diverges. 5 Σ 5n2+5 n =1

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A: The given series is ∑k=0∞-16k. To check convergence of the series we use ratio test. Suppose we have…

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Q: 33 f(x) = sin 2x + Ve2x + 2x – In e, x # 1 1-x

A: derivative

Q: x² sinh x dx

A: Let's find.

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Q: Convert thepoint (x,Y) from rectangular to polar Coordinates Cr,e). 4)(2,-2)

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Q: 4x? ds where Cis the portion of the curve y y° 1 =- from Evaluate the line integral (1,1) to (2,4).

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: 14

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Q: 1. Determine the absolute extrema of f(z) = (sin a – 1) cos z on -. 2 if they exist, and identify…

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Q: Explain why the integral is improper. 25 05 O At least one of the limits of integration is not…

A: Here, the given integral is: ∫091xdx

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Q: dz (a) Find of the following functions: dx zx2+1cos y? = sin(y? + 22z)

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A: We have to find the volume of the given region according to the given information

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A: Let's find.

Q: Find the radius of convergence, R, of the series. (x + 6)" 6" n = 1 R = Find the interval, I, of…

A: Consider the power series           ∑n=1 ∞ an(x-a)n then , series convergent if x-a<R , where , R…

Q: (2x3 – xy? – 2y + 3)dx - (x²y + 2x)dy = 0

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Q: Find the arc length L of the graph of r(t). r(t) = 6 cos(t)i + 6 sin(t)j + tk, 0<t< 2n 0 <t< 2n L =

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Q: Calculate the iterated integral. 36 9. )dy dx + 1

A: Given problem:-

Q: Choose the rule that you would use to most efficiently find the derivative of the function 3 f(x) =…

A: The given function,   f(x)=32-x3

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Q: Σιο.1-1+ 0.9" n=1 Determine whether the given sequence converges or diverges. If it converges, find…

A: To find whether the sequence ∑n=1∞0.1n-1+0.9n converges or diverges   The given series is sum of two…

Q: Find the curvature K of the curve. r(t) = 9 cos(nt)i + sin(at)j K =

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Q: The one-to-one functions g and h are defined as follows. g (x) = 3x+13 h= {(-8, -3), (-3, 2), (3,…

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A: Let's find.

Q: List the first 5 terms of the sequence. 1 22 3n 3n3 32 3n n2 3n (b) -2)n+1 + 3" (a) an =

A: For (a), Given: Now, an=13n3+223n3+323n3+...+n63n3   =13n31+22+32+...+n2   =n+1n+22n+363n3…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A: Symmetric equation of a line passing through the two points P(a,b,c) and Q(p,q,r) is given by,…

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Q: Verify that the two planes are parallel. --x + 6y + 2z = 7 *+ 3y + z = 8 Find the normal vector, n,,…

A: The normal vector to the plane ax+by+cz=d is given by n=a,b,c

Q: f (x) = x²In x + sec x; find f"(x)

A: Given ,f(x)=x2ln(x)+sec(x)DIferentiate…

Q: Use the Product Rule to find the derivative of the function. g(x) = (x2 - 2x + 5)(x³ - 6) g'(x) =

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Q: p(x, Y, z) 4 – x2 – y²

A: Given problem:-

Q: п+1 Given that 0.47199 determine the value of ) n +1 n3 n=3 n3 n=5

A: Given: ∑n=3∞ n+1n3 =0.47199 To evaluate: ∑n=5∞ n+1n3

Q: 2x) dx Find an approximation to the integral using a Riemann sum with right endpoints and n = 8.

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Q: dx 7. S; x³ Vx2-4

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Q: Find the intervals on which f is increasing and decreasing. f(y) = sin y - y cos y on 2' 2

A: Find your answer below

Q: Eliminate c from the equatia cxy + c²x + 4 = 0. O x* (y')? + x?yy + 4 = 0

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Q: Examples: Find the limits of the following: 1. lim sin x = sin1 = 2 5. lim sec x = lim cos(-) = cos0…

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Q: a) | f(x)dx = b) | f(x)dx = c) 5f(x)dx =

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Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). %3D v= (0, 6) %3D b =

A: Explanation of the answer is as follows

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Q: In R³, consider the triangle formed by X (2,0, 4), Y (0,5, 0) and Z (-2,0,0). Us- ing vector and…

A: Let's find.

Q: Find the gradient of the function at the given point. 2 = In(x2 – y) - 9, (2,3) Vz(2, 3) = Need…

A: This is a problem related to derivation. Please follow the procedure given below for solution.

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Q: 1) (a) Convert BOTH of the below equations from either polar to rectangular or rectangular to polar.…

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Q: dy = 3 , find dt dx when x = 1 dt x and y are functions of a third variable t. If Væ + Vỹ = 4 and

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Q: y y=x+1 x= 4 y = 0

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