(i) At x = 1, the Fourier Series of f(x) = converges to: (A) 0 (B) 1 (2-2x, -1

Q: Find the area bounded by the curves -x + y² = 8, x = -2y and y = -2.

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Q: II. Consider the polar curves C₁ : r = 3 (in blue) and C₂ : r = 2-2 sin (in red) and let R be the…

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Q: Find the volume of the solid generated by the region bounded by -x + y² = 8, x = −2 and y = -2…

A: Follow the steps

Q: *Problem 3.2 Consider the collection of all polynomials (with complex coefficients) of degree < N in…

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Q: 6. Let S be the surface with equation 4y² + 4z² − x² - 16 = 0 a. Find an equation of the trace of S…

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Q: Z=x+y+ cos(x+y)

A: Given,        z=x+y+cos(x+y)

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: we are given a solid and we need to find The Centroid or center of mass.   About the solid in…

Q: be roots of unity and let a =

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Q: what is the unit of the final answer?

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Q: 4. Evaluate the line integral along the path C given by x = 2t, y = 10t, where 0 ≤ t ≤ 1. (a)…

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Q: be an open subset in C and f

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Q: 1. Use Cramer's Rule to solve the below given problem. 4 5 -2 11 A = 7 12 -6 X = 49 2 6 0 8

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Q: a. Identify the type of graph of S b. Write the equations of the traces of S on the coordinate…

A: Note that : x2a2+y2b2-z2c2=1 represents a hyperboloid of one sheet.

Q: Allow A be the point with Cartesian coordinates (6, 9), and D be the plane curve with parametric…

A: The slope of the tangent to the curve: y=fx at x=a is f'a. The point-slope form of a line that…

Q: Q5: Consider the following subsets of real plane R² Determine with graph: 1-Arewise connected A=…

A: Follow the steps.

Q: Let f: MM' be an R-module homomorphism, then

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Q: Let M be a matrix a M-[b] = c d Matrix M is non-singular if and only if O ad + bc #0 O ad - bc #0

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Q: ) Using each graph of y = f(x), sketch th [(x) and g(x).

A: (a) Given,

Q: Every Möbius transformation which

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Q: 2 2 3√2 2. Consider the polar curves C₁ : r = 4 + · cos 0 and C₂:r = 2 − cos as shown in the figure…

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Q: A 40-m high tower stands vertically on a hill side (sloping ground) which makes an angle of 18…

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Q: 1. Evaluate the line integral of E-xa, -y a, along the segment P; to P; of the circular path as…

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Q: Q5: Consider the following subsets of real plane R²¹ Determine with graph: 1-Arewise connected A=…

A: Here we have a common point in both of the sets. Also thos two sets are individually connected.

Q: Find (x, y): R = {(x, y): 0 ≤ y ≤ √√x² +1,0 ≤ x ≤ 1} about the x-axis.

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Q: x² (Figure 24). Verify the 1) Let f(x) = following: X 1 (d) y = x + 1 is a slant asymptote of f(x)…

A: This is question from topic asymptotes.

Q: Consider the vector-valued function R (t) = ( 8/3 t 3− t, 2t2 , 2 − 2t2 ) - Find II R(t) II…

A: We are given R(t)=(83t3− t, 2t2, 2 − 2t2) to find II R(t) II and distance traveled by a particle…

Q: 8). Prove the validity of the arguments using the method of conditional proof. a). p → q (qvr) → s…

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Q: d) y'= 4y-3x 2x-y

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Q: Find the Area of the Surface obtained by rotating the curve about the x axis y = cosh x, 0≤x≤1

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Q: 8 (1) = {(In(3-1) 141-13, 38²2-8), t), ‚31² t (0,−1, 4), t . Find the domain of Ř.

A: This is a problem of vector calculus.

Q: Let C be a curve with the parametric equation in the given. a. Set-up the integral that will give…

A: Set-up the integral that will give the length of C and Determine (algebraically) if C is concave or…

Q: 2. y" - 6y +9y = 2 sin 3x; y(0) = 1, y'(0) = 1

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Q: A person borrowed 500,000 pesos at an interest rate of 18% compounded monthly. Monthly payments of…

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Q: Find the volume of the solid generated by the region bounded by y - x² = -3, x+y = 3 about y = -5.

A: To find the volume of the solid generated by revolving the region: y-x2=3, x+y=3 about y=-5

Q: 6. Let {V1, V2,..., Un} be a basis for Rn. Let T: RnRn be a linear transformation which is one-one…

A: It is given that v1, v2, …, vn is a basis for ℝn. Let T:ℝn→ℝn is a linear transformation which is…

Q: Considering C is a curve which has the following parametric equations: x(t) 1 = t³ − t+1, C = tER…

A: Given curve is  C=xt=13t3-t+1,yt=t-tan-1t,t∈ℝ

Q: sforms in finding the solution to the giver +4y= 4e²t. v(0) = -1.v'(0) = -4

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Q: The population of a town is decreasing at a rate proportional to its size. In 1980, the population…

A: Given that  The population is increasing proportionally, given that in 1980 population=50000,…

Q: VI. Let C be a space curve defined by the vector-valued function R(t) = (sin t cost, sin² t, √3t).…

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Q: Use Lagrange multipliers to find the maximum area S of a rectangle inscribed in the ellipse x² 1² +…

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Q: find these thin ou will need to create a table with the following information for each cub 1. Side…

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Q: Resume 1.pdf Use Venn Diagram to find answer to this question. In a party we have these people: 35…

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Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: Solution:x2+y2-4y=0, y=4-x and axis of revolution y=0above equation x2+y2-4y=0 can be written as…

Q: Find the area bounded by the curves y - x² = -3,x+y = 3 and y = 0.5x.

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Q: Evaluate be (x² + y²) ds, C is the right half of the circle with radius 3 centered at (0,0). Hint:…

A: Solution:-

Q: Let {fn} be a sequence of complex-valued continuous functions on CC. If {fn} converges uniformly to…

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Q: 4. Prove that the L{2t²} = 4 S3

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Q: ) An edge of a connected graph is called a bridge, if removing this edge makes the graph…

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Q: In the diagram below, T≈ ZW, LUX. Enter segments in the blanks provided that would result in a true…

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Q: Let S be the surface with equation 4y2 + 4z2 - x2 - 16 = 0 1) Find an equation of the trace of S on…

A: