Find the centroid of the area under the curve y = x² from x-2 to x-4.

Q: E(0.1)" -1 + (0.9)"] n=1 Determine whether the given sequence converges or diverges. If it…

A: Given series ∑n=1∞ (0.1)n-1 +(0.9)n

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

Q: ピ+5 1 lim t一+0|5t2 +6'2t (?, ?)

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Q: Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer…

A: A vector valued function in the form of  r (t) = f(t) i +g(t) j +h(t) k is continuous at the…

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: 1. Given z, = 5 cos 377 +i sin 37 and z2= 37 +i sin 2 find z,z2 where 0se< 2x. cos 2 2 37 +i sin 2…

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Q: (e) Alternating Series Test: Σ (-1)"-2 3n + 3n

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Q: Find the Taylor series centered at r 3 for the given function. f(r) = In(x + 2) a) Find the…

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Q: Consider the following function. f(x) = -x2 - 10x – 9 Find its average rate of change over the…

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Q: Determine if the given sequence converges or diverges. If it converges, what is its limit? 5+ 3n3…

A: As you have asked for the solution of questions a -c only. So I am solving those only. Thank you.…

Q: For each of the following series determine if the series converges c for series convergence or…

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) V…

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Q: A racecar travels northward on a straight, level track at a constant speed, traveling 0.750…

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Q: Let f be a twice differentiable function such that f(1) = 2 and f (3) 7. Which of the following must…

A: We have to choose correct option  Here using Lagrange mean value theorem

Q: a) f(x)dx = f(x) b) f(x)dx = y = f(x) Area A = 1 Area B = 2 Area C = 2 | 5f(x)dæ = A c) Area D = 0.6…

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Q: Consider the following. u = 9i + 5j v = -8i + j + 6k Find u x v. 1li – 54j + 49k Determine if u x v…

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Q: Convert the point (r, 0) from Polar to Rectangular Coordinates (x, y). 1. (3, 7/6)

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Q: Eliminate the constant 'a' from the equation (x – a)2 + y? = a² O (x? - 2y)dx + 2xydy = 0 O (x2 -…

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Q: Find the derivative of the function described. (Rx5) 1. y = (2x + 3) (5x – 4)

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Q: sint In(cos t)dt

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Q: A region bounded by f(y) = 2y, y = 1, y = 3, and x 0 is shown. What is the volume of the solid…

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Q: 1. Consider the graph of the function f(x) = 1.a. Is the function f (x) continuous at x = 1? Justify…

A: We need to find if the function is continuous or not in given interval.

Q: dx 7. S; x³ Vx2-4

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Q: Find the following. u = (0, 1), v = (5, -3) (a) |u|| (b) ||v|| (c) |u + v|| (d) |u| M (e) U + V (f)…

A: We can solve this as follows:

Q: Use limits to determine all the linear asymptotes of 3r2 if I1. x² + 2x – 3'

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Q: F (x, y, z) = x²yz² – 3xy°z + 2y°z²

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Q: Solve the following system of differential equations. dx —х — у, || dt dy Зх — у dt

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Q: If L is a line in 2-space or 3-space that passes through the points A an B, then the distance from a…

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Q: Find f (x) if f'(x) = and f(1) = 25. O f(x)= 16x + 25 O f(x) = 16x +1 O f(x) = 16xl +9 O f(x) = 16x…

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Q: f (x) = (x³ – 5x + 2)(x² + x – 7); find f'(x) %3D

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Q: 5x(V1 + x-) dx

A: This question can be solved using the concept of integration by substitution.

Q: Consider the following. u = (2, -1, 0) v = (-2, 3, 0) Find u x v. Determine if u x v is orthogonal…

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Q: The graph of x? + y² + 2y – 8x + 17 = 0 is a circle. O FALSE O TRUE

A: The given problem is solved below in detail.

Q: 1 Evaluate lim Gnx x→1+ 'Inx х-1

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Q: (c) f(x, y) = V3x + y?, x = 2, y = 0, dx = 0.01, dy = 0.01. %3D %3D 1 f. 2/3x + y? 3 (i) 3x+y? (ii)…

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Q: Solve the initial value problem 2x(y + 1)dx – ydy = 0, where x = 0 and y = -2. x² = y – In[y + 1] +…

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Q: Given the series: 1 1+ - 6. 1 1 + ... 36 216 does this series converge or diverge? O diverges…

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Q: given magnitude and the same direction as u. Magnitude ||v||-5 Direction u- (-4, 6, 4) Submit Answer

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Q: Solve the following differential equation using variation of parameter. 4y" – y = xe"/2; y(0) = 1,…

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Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows:

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: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: The given parametric curve is: r(t)=cos(πt)i-ln(t)j+t-10k

Q: 4. S ( 12 x³ + 15 x - 20 ) dx 5. S 10 x2/5 dx 6. § 3 ³V x8 dx 7. S ( 8 + 2 dx x3 x4. 8. S ( 2x³ -…

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

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

A: -x+6y+2z=7 ------(1) normal vector n1 for plane -x+6y+2z=7 n1=&lt;-1,6,2&gt;   or -1 i+6 j +2 k…

Q: dx x2 + 6x + 25

A: This question is based on definite integral.

Q: Question For the function given below, which statements concerning Rolle's theorem are true? f(x) =…

A: f(x)=x3-16x+2    ;  [0,4]

Q: Determine if the sequence is increasing, and/or bounded. 3 — п (b) { (a) 1 — Зп - 3n n=1

A: Given

Q: I = -2+3s z + 4 1. Consider the lines defined by the equations l : x – 2 = y – 1= and l2 : y = -1+ s…

A: Given:  l1= x-2 = y-1 = -z+42=tl2= x+23 = y+1 = z-2-4=s

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

A: Given: Now find the x-intercept of the line y=x+1. y=x+10=x+1x=-1x,y=-1,0 Now taking an elementary…