Find a power series representation for the function H(x) = S" arctan(z²) dz. And Find the 7th degree Taylor Polynomial T7,0(x) for H(x) = J, arctan(z²) dz.

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Q: 8. Let f: R-→R be a field homomorphism. Show that f is identity.

A: Introduction: Like integral domain, a field also have homomorphism. A map f:F→K is referred to as…

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Q: x+y Value of 5x+4y 4x 2xis: 10x+8y 8x 3x (a) 0 (b) x (c) y (d) none of these Select the correct…

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Q: 2 : 1+ai and w=2-i which of the following is equivalent to ū 9. I+i c. 1-i 6. - 3 +i d.1-3i

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Q: Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R =…

A: We find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q =(4,-2,1)…

Q: T(n)=2T(n-1)-T(n-2), T(0)=1, T(1)=1.

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Q: Q7) by using the (graphical method) find the optimum solution of X1, X2 that the maximum Z=5X+7Y…

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Q: A Moving to another question will save this response. Quèstion 3 Evaluate : dz where C is the cirlce…

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Q: SAP

A: Given, f has a derivative on an interval I, and f' has successive distinct zeros at x=1 and x=5. To…

Q: 80 24c 80 C = 24 Write the 80 as the product of 5 and a power of 2. Write the 24 as a factorial.…

A: This is a problem of Taylor's polynomial approximation.

Q: f(t) = e4t cos 3t 3 s-4 A. s2-8s+25 С. s2-8s+25 3 s-4 В. s2-8s-7 D. s2-8s-7

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Q: 1/4 1. Find all the values of 3.

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Q: 1. The coefficient a, of the Fourier series of the periodic function f(t)= (2t 0<t<2 0 2<t<6 is…

A: Some of the books use the Fourier series as first coefficient a0, some of the books use this as…

Q: 3. Decrypt the letters XMMIFZXQFLKP if it was encrypted using an alphabetic Caesar shift cipher with…

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Q: A house and lot with the original price of ₱2,300,000 was sold at a discount price of ₱2,150,000.…

A: The formula to calculate the discount rate is Discount %=discountoriginal price×100%.

Q: Problem 1: Given: -2,3,8, 13, ... Find the following: (a) 6th term of the sequence; (b) an formula…

A: Here we use arithmetic progression.

Q: Let {xn} be a bounded sequence of real numbers. Prove that {xn} converges if and only if lim inf xn…

A: Proof

Q: 6° Szx dx t yay where L cs parabol y=-x(x-) arc

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Q: d. 20 ( cos 120° +isin 120°) Based on De moi vre's theorem, the given below is equi valent to whi ch…

A: Let , z = 5cos 30° + sin 30° which is in polar form of complex number. Compare with , z = r cos θ +…

Q: Find all the solutions r E Ziz to the equation r³ – 5x² – 7x = 0 mod 13.

A: First, solve in real number then ring down to the finite field.

Q: How much is the minimum cost for this assignment problem? 87 89 O 92 O 94

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Q: 10. Which of the vectors U =, V = and W = are in the same plane?

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Q: Let so and A be positive numbers and consider 4). 1 Sn+1 = n 2 0. Sn Sn 1 (a) Show that sSn+1 2 VA…

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Q: Consider a probability space (N, F, P) and a random variable X e L-0, F, P). solution to only b…

A: Given: Let's determine EEXGH=EXH

Q: Solve the differential equation of dy/dx + 1/3 y = e^x y⁴

A: Divide both sides of the given differential equation by y4 to obtain the right hand side y free.…

Q: Consider matrix A = and vectors x = and y = Calculate matrix B = (A – A")? and vector w = Bx. Then,…

A: To find matrix B , vector w and the scalar product w•y.

Q: Consider the sequence {a„} where a, is given by (n³ – 1)/nº, (n² + 1)/n², if n is even. if n is odd,…

A: The given question is related with  sequence. Consider the sequence an , where an is given by…

Q: The system of linear equations: X1 + 2x2 + 3x3 = 2 X1 – x2 + 2x3 = 1 Select one: О а. is an…

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Q: (iii) 1 + 1 33 + ... 22 + 22 33+

A: given series test for comparison tests - apply this comparison test to a given series the auxiliary…

Q: x+ 2 2x – 3 x+1 4 If A = is symmetric, then what is x equal to? | 1. 2 2. 3 3. -1 4. 5 Select the…

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Q: 3) Show that (a + bi)º = (a – bi). Hint: for any x, y in a field containing Fp, (x+y)º = xº + yP.…

A: As per our guidelines, we are supposed to answer only one question if there are multiple questions…

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Q: Define analytically the periodic functions shown. 1 f(x) 2 2 4 6 8 -1

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Q: 6- If a,b,c,d>0, use the properties of logarithms to simplify and then Tnd the exact numerical value…

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Q: Express the sum of integrals as an iterated integral in polar coordinates: r2V3 4+V16-x² x dx dy +…

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Q: 5. Consider the vector space P2 along with the subspace, H = span {1+21°, 2. -ť,1-f} Use coordinate…

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Q: Show that in the factor ring Z[i] / , the element x + is a unit.

A: Given a factor ring Zx2x+1=a0+a1x,+⋯+2x+1 |a1∈Z  As 2x+1+2x+1=0+2x+1 Since,  2x+1∈2x+1   as aH=H iff…

Q: Value of cos15° sin15°| is: sin 15° cos15 (a) 1 (d) none of these Select the correct response: a

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Q: Consider the following two matrices: -2 -1 1 0) C = 7 -1 D = 3 3 -2 1 Which of the following four…

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Q: Compute the following limits using L'Hospital's rule if appropriate. Use INF to denote oo and MINF…

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Q: PROBLEM # 1 t3uy +5uz, FOR THE VECTORS A= Ux B= 2 Ux + 4uy + Guz, and C=3ux +4uy +5uz, Sko SHOW THAT…

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Q: Yumi wants to buy a volleyball. Its original price is ₱965 and is on sale at 25% discount. How much…

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Q: Given the following matrices, perform the indicated matrix operation. 1 8 [5 1 -2 -9 7 1 2 -2 -4 5…

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Q: [17] For each of the following equations, • find general solutions; solve the initial value problem…

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Q: (a) (AN B)':

A: This is a problem of set theory.