Evaluate the following integrals using contour integration ( 1 -dx 13+5sinx

Q: 5. Graph the polar function r = sin 20.

A: Curve tracing is a rough diagram structure or shape of the plane curve given its equation without…

Q: Find the mass of a thin funnel in the shape of a cone z =√x² + y2, 1 ≤ z ≤ 3, if its density…

A:

Q: 1. Solve the initial value problem: y" - 6y' +9y = 11e³x 43 y(0) = 2/1/1, y '(0) = 14/2/2

A:

Q: +|m₁nEN ² mine 3. Let S = { (-1) ²² [ +1 +224131 Find all cluster points of S

A: S=-1m+n21m+2n+12n+3 m,n∈ℕ

Q: you have spotted a new pair of shoes that you really want to buy, but they are too expensive. The…

A:

Q: Find the rest of 777 in the division by 3864

A: Solution :- Rest of 777 in the division by 3864First calculate 77=823543Now to find the rest of…

Q: A critical point will be a point of inflection if the second derivative is Higher than first…

A:

Q: 6. Use the method of Lagrange multipliers to find the maximum and minimum of f(x,y)=x+y subject to…

A:

Q: Evaluate • [[F · ds, where F = and S is the helicoid with vector equation , 0≤ u ≤ 2, 0≤ v≤ with…

A:

Q: A corporation starts making monthly payments into a sinking fund in order to have $463,000 in 11…

A:

Q: Using the hypothesis method, Solve the following equation: 2 (D²₁ (D³²-1) Y = x ²

A:

Q: 2. Prove that the series (111 is not absolutely Jn (Inn13 Convergent. M=2

A:

Q: True or false. Please provide the reason if the statement is false. Let Q be a mxn matrix with…

A: Let Q be a matrix of size m×n with orthogonal columns where m≥n. To Explain: whether the given…

Q: Let f: (– 2,2) → R be defined by f(x) = (n+ 1)_x". Find Σ n=0 2⁰ 1 f f(x) -1 f(x) dx

A: Given:f : -2, 2 → ℝ is defined by: fx=∑n=0∞n+12nxn To Find: ∫-11fxdx.

Q: Request explain beginning of step 3 as to how do we get a=b and the second relation involving roots.…

A: -a+ia3+2b-c+ic3+2d=-1+3i2⇒-2a+i2a3+4b=-1+3i-c+ic3+2d⇒-2a+i2a3+4b==c-ic3-2d-ic3-3c+2i3d⇒-2a+4b+2c+2d+…

Q: 2-22 ( -k (k>0), then prove that points A(z₁), 2-2₁ 3-22) B(z₂), C(3), and D(2) (taken in clockwise…

A:

Q: Evaluate the surface integral. 11. ³² ds. y² dS, S is the part of the sphere x² + y² + z² = 1 that…

A:

Q: In the field of the integers modulo 17, 6-¹ is a. 3 b. 6 c. 11 d. 12

A:

Q: Problem 1. 92x² + (a) If A is diagonalizable, that is A = ODO¹. Assume a polynomial f(x) = ao + ₁x +…

A:

Q: Find the surface area of the helicoid (spiral ramp) with vector equation F (u, v) = (u cos v, u sin…

A: Given, r¯(u,v) = ucosv,usinv,v, 0≤u≤30≤v≤3π   We have to find the surface area of the helicoid.

Q: If a pesticide released during a dawn (6 am) crop spraying event is present at 55 mg/L in a pond…

A: To find the rate constant for the degradation of the pesticide, we need to first find the…

Q: Find the change of variable x = Py that transforms the quadratic form x¹ Ax into y¹ Dy as shown. -…

A:

Q: 4) Minimum Spanning Trees. Find a minimum cost spanning tree on the graph below using Kruskal's…

A: Weight of the minimum spanning tree

Q: Prove that's is prime p, then (a + b)² = (a² + b²)(mod p), Va; b € Z

A:

Q: 6. Find the sum of each of the following. (a) Σn(n − 1)x" (b) Σ n n 3P

A:

Q: Find second iteration y₂ of the trapezoidal method for y' = (x + y)x, y(2) = 3 Ax = 0.2

A: Definition follows

Q: Are the vectors u = [3_2_0],7 = [-3_5 −4] and @ = [1 0 -2] linearly independent? linearly…

A:

Q: Use the divergence theorem to find the outward flux of F across the boundary of the region D. F =…

A:

Q: Prove that a group G is abelian if and only if the mapping f: G→G, given by f(x)=x-1,  is a…

A:

Q: The molecular formula of a compound is C6H1002. What is the corresponding empirical formula?…

A:

Q: Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until two…

A:

Q: If D=- dt find a complete solution of: (2D+3)x+ Dy=1 (2D+3)y-z = e' 3Dx+3z = 0

A:

Q: Calculate the rest of 12021 + 22021 + 3202¹ by dividing by 11

A:

Q: The cuberoot of a number can be approximated by the recursive formula 13 (25 Sn where so is the…

A: The given recursive formula is  sn=132sn-1+Asn-12 Our aim is to find the second iterative value of…

Q: Evaluate the surface integral. [[ xz dS, S is the part of the plane 2x + 2y + z = 4 that lies in the…

A:

Q: Consider the following matrix: -18 0 5 0 20 -30 -3 10 0 40 0-30 0 A = 0 0 0 0-30 -15 0 5 0 17 a)…

A: A=-1805020-30-31004000-300000-30-1505017

Q: please show all work 4. Consider points A(2,−3,0) and B(−1,2,1). Let u be the vector connecting…

A:

Q: Consider the function f defined on the interval [0, 10] as follows, 10-13% f(x) = 5 x = [0, 5], 2, x…

A: Given That : Function f=25xx∈0 ,52x∈5 ,10 fx=∑n=1∞cnyx -y''=λy , y0=0 ,y10=0 To Find : Coefficient…

Q: Let R denote the ring of integers modulo 48 and S denote the ideal (0, 16, 32). The order of the…

A:

Q: If one of the vertices of the square circumscribing the circle |z1|= √2 is 2 + √3i, find the other…

A:

Q: Consider the following vectors: -9 -6 THE a= C= -6 -7 -6 For each of the following vectors,…

A: a→=3312, b→=-9-6-6-5, c→=-90-7-6

Q: A. Show that any sequence of positive real numbers either has a subsequence that converges, or else…

A: Construct a new sequence which is easier to study.

Q: Find O d² cot 1 ¹x dx2 -2x (1+x²)² 2x (1+x²)² -1 (1+x²)² -2 (1+x²)²

A:

Q: Consider the following matrix: 30-8 -4 03 8 4 0 0 11 4 0 0-24 -9 A= a) Find the distinct eigenvalues…

A: Diagonalization of the matrix

Q: /(x (x2.1 + x-1.3) dx

A: Solution

Q: Prove that fo f = Idom f iff f-¹ is a function from ran f to dom f.

A: Prove That : f-1of=Idom iff f-1is a function from ran f to dom f.

Q: 3. Reduce each of the following to the smallest non-negative residual. (a) 87122 mod 23 (b) -7823…

A:

Q: Let * be defined on Q+ by a*b = Determine whether the binary operation * gives a group structure and…

A: A binary operation * is defined on the set of positive rational numbers Q+  as a*b=ab2. Our aim is…

Q: Use Gauss's law to find the charge contained in the solid hemisphere x² + y² + z² s a², z ≥ 0, if…

A:

Q: Find the rest of 777 in the division by 3864

A: Solution :- Rest of 777 in the division by 3864 First calculate the value of 77=823543Convert the…