Assuming x E Z. Prove

Q: 6. If a series £u, converges to the sum u then so does any series obtained from Eu, by +he torms in ...

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Q: Question 55. Suppose y(x) is the solution to the given initial value problem dy (In x)s y(1) = 2 dx ...

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Q: Consider the function g(x, y) = tan¬(1 – x) + 3e2"-y and the point P (1, 2). %3D a. Use the lineariz...

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Q: rs can be represented

A: Non- terminating decimals, The number will never ends after the decimal is said as  non- terminating...

Q: 7. (a) Write the following in reduced row echelon form. Find a basis for the (b) nullspace, (c) row ...

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Q: If in an AP the sum of m terms is equal to n and the sum of n terms is equal to m .then prove that t...

A: Let us consider the AP a, a+d, a+2d, a+3d,...... The nth term is obtained as  an=a+(n-1)d The sum of...

Q: How many turns would be there in the polynomial function of degree 3?

A: Concept: Various graph of diffrent polynomials is explained below:

Q: facR,af ischiffontiable at xo gisdiffera tible at to anol

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Q: Show that if (aib- 2 for all a,b EG draip (G,)is abelian if and od

A: To show: A group G,∘ is abelian if and only if a∘b2=a2∘b2 for all a,b∈G.  

Q: Q4: Solve the following integrals:- dx 4dx (1) S: (2) S: sec xesin x (3) S x sec? x dx 2+cos x

A: Note:-  As per our guidelines, we can answer the first three sub-parts of this problem. For the rema...

Q: Problem 2. Verify that each given function is a solution of the given differential equation. Through...

A: Given: The differential equation, x2y''+xy'-y=lnx The functions, y1=x-lnx and y2=1x-lnx   To verify:...

Q: A = -3 4 3 0 -1 1 -3 3 1 4 -3 9 1 3 -1 3

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Q: C. Find the volume of the solid whos base is bounded by the graphs y%=1and y=x-1 The crosS sections ...

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Q: Graph the feasible region for the follow system of inequalities by drawing a polygon around the feas...

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Q: If the sum of first n even natural number is 420,find the value of n

A: Problem:- If the sum of first n even natural number is 420,find the value of n first n even natural ...

Q: 5. your answer. If they are not then supply a proof of the claim. Which of the following pairs of gr...

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Q: 2. Given the following possible solutions to a differential equation. A. y = 2sin (x) B. y = 2cos (x...

A: Given the differential equation yy'+2sin2x=0We have to find these following solution satisfy differe...

Q: Find the value of J/2(x)

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Q: =3n² + 3n 2. 2 3+6+9+...+3n cam

A: We have to prove that the equation 3+6+9+.....+3n=3n22+3n2 holds by principal of mathematical induct...

Q: power expansion of (e^x)/1-x

A: Given f(x) = ex1 - x

Q: of equa = 1 3z = 5

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Q: The set S contains some real numbers, according to the following three rules. (i) 1 1 is in S. (...

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Q: QUESTION: Let U be a finite dimensional vector space over F with basis By : U1,….., Up. Let SE L(W,U...

A: Given U be a finite dimensional vector space over F with basis u1,…,up. Let S∈LW,U, where W is a vec...

Q: 16. Prove: If A is an eigenvalue of A and x is a corresponding eigenvector, then s) is an eigenvalue...

A: We will use definition of eigen vector to prove the result.

Q: H.W. 1- Solving the above example during (n=3, 7) and compare with each integral result by Simpson R...

A: We can solve this by using Simpson rule  

Q: 4. The perpendicular offset of the PT of a simple curve is 120.20m. If the angle of intersection is ...

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Q: prove that C+Ã +3 = ARC Using the truth table

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Q: a. (x² + y?)dx + 2xydy = 0 a?u b. ax2 a?u a?u = 0 əz? ду? c. yy"= x d²y d²x d. x +y dt2 C1 dt2 e. y"...

A: The order of a differential equation is defined as the order of derivative.

Q: Prove that for any integer a, 3 divides

A: To prove that for any integer a, 3 divides (a-3)(a+4)(a+2).

Q: d WX)=y, y2" -V½ y,". Let W(x)=W[y, Y½] for any two differentiable functions, Then dx Select one: O ...

A: Introduction: The Wronskian is the determinant of functions and their derivatives. Suppose, S=y1,y2,...

Q: (b) Find the area of the triangle whose vertices are A(0,0,0) ; B(1,1,1) and C(0,2,3). 1 (C) Find th...

A: Given (b) The vertices are A0,0,0, B1,1,1, C0,2,3 c(1) y=1x2-1 c(2) y=9-x2

Q: Find a particular solution to y" + 4y + 3y = 3te". %3D

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Q: Q2: find the integral of trigonometric function cos sin* dx

A: Given the integral is ∫0πcos5xsin4xdx

Q: 1 Q1. Find the principal value of (3 + 4i)7. Show details.

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question s...

Q: Determine the form of a particular solution y, (x) for y" - 4y'+5y e*+xsin 3x- cos 3x. [Do not evalu...

A: Solution: The given differential equation is y''-4y'+5y=e5x+x sin3x-cos3x. For the complimentary fun...

Q: What exactly is the Modulus operator?

A: The modulus operator is typically used on integer operands but is defined for floating point numbers...

Q: Show that if n is a positive integer, then n is even if and only if 7n + 4 is even.

A: Given: Show that if n is a positive integer, then n is even if and only if 7n + 4 is even  

Q: Prove the theorem of division algorithm - If a and b are integers such that b>0, then there are uniq...

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Q: s the cost function of e number of units pro aximum profit? Wha

A: Let x=q. Cost function of of the product is  for q units produced.  Selling price for 1 unit is 2 T...

Q: The equation for the line that passes through the point (1,0) and perpendicular to the --1 is line x...

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Q: 5. Use the result of the previous problem to calculate the area of the hypocycloid z²/3 + y2/3 = a²/...

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Q: ) Assume (X,A) is a Ealgebra and ld ycx be an anbitrary subset. Show that the Pami ly of sets 3{unyl...

A: σ-algebra: a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X, is closed under ...

Q: 2. Using the iteration method to find the approximated root of the following equation: (x-1)e-1-0 Co...

A: Given: The equation, x-1ex-1=0 and the iteration equation, xk+1=1+e-xk.   To show: (1.) In the inter...

Q: ebt + e-bi ebt – e-bt Find the Laplace transform of coshbt. Recall that coshbt = - and sinhbt = 2 2 ...

A: Given coshbtWe have to find the Laplace transform and in following of them.L{coshbt}=sb2-s2L{coshbt}...

Q: 15. Find the eigenvalues and bases for the eigenspaces of A A =

A: The given problem is to find the eigenvalues and eigenspaces of the given matrix A.

Q: The following questions consider the wind speeds of Hurricane Katrina, which affected New Orleans, L...

A: We will use the given table and formula for differentiation to calculate what is required.

Q: 8. (a) Write the following in reduced row echelon form and (b) find the rank and nullity of the matr...

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Q: Using integration by parts, find the Laplace transform of the given function; n is a positive intege...

A: Given f(t)=tneatwhere n is a positive integer and a is real constant. We have to find the Laplace tr...

Q: Let T: R? - R? be a linear transformation that sends the vector u = (5, 2) into (2, 1) and maps u = ...

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