Verify the product law for differentiation, (AB)' = A'B + AB' where A(t) = B(t) = 1-t 1+t 21² 21³ 3 t 2t - 1 A +³ t and

Q: 13. If n is a square, show that d (n) is odd. 14 TC

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Q: Shown beside is a curve called "lemniscate", given by 2(x² + y²)² = 25(x² - y²). A) Use implicit…

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Q: Use spherical coordinates to find the volume of the region outside the cone p=1/4 and inside the…

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Q: Find a positive value of k for which y = sin(kt.) satisfies 22 k d'y dt² +y=0.

A: We have to evaluate the value of k such that solution  satisfies,differential equation…

Q: Let K be a finite normal extension of a field F. If a, ß are any two elements of K conjugate over F,…

A: Statement : Let K be a finite normal extension of a field F. If a and b are any two elements of K…

Q: Find f and f, at the given points. ㅠㅠ (a) f(x,y) = rysing; 2¹2 (b) f(x, y) = 2x 1-y ; (1,0)

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Q: (c) y""+y" = ex cos x

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Q: Check if the sequence is uniformly convergent using the steps listed below: n+sin(nx) b. fn (x) = "…

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Q: orthogonal group O(n) = {A E GL(n, R)| AA = A'A

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Q: Determine all values of a for which the following set of vectors is dependent or independent. You…

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Q: 1. A professor is buying breakfast for his students as a way of saying Thank you for a good…

A: 1) Calculate the number of students who want either cereal or bacon using the Principle of Inclusion…

Q: a) Differentiate the function Q(p)= -2√/p³ (e-P-P). b) Hence or otherwise, determine Q'(1).

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Q: The curves f(x)= 3-x^2 and g(x) =e^(2x)-1 are shown in the figure. Let R be the shaded region…

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Q: Determine the sum of the following series. Σ(119)

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Q: The masses m, are located at the points P₁. Find the moments Mx and My and the center of mass of the…

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Q: I 4. Given differential equation y" + 4y = sec(2 t) a. Find the complimentary solution y, that…

A: We have to find (a) complimentary solution(b) particular solution using variation of parameters…

Q: A 100 gram mass, when attached to a spring hanging vertically, stretches the spring cm. The mass is…

A: Hooke's Law relates the force exerted by a spring to its displacement from equilibrium:F=−kxwhere:F…

Q: л - Ca] - [[5]74 +y poolf

A: Definition used

Q: is an approximate identity as 1-o i.e. 1 x lydy 1o, prove that ₁ (y) = -=-³x²₁x₁² e ₁) = 1

A: If  then each component of y is independent. So if we consider each component of y is normal…

Q: A. -1 C. 0 -1. -3. 1. Consider the following differential equation: y" - 4y' + 5y = 0 a. Write the…

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Q: Ethan Steel, Inc. has three factories that manufacture steel components for three different rail…

A: ProjectFactoryABCMaximum Capacity178230002654500031963000Demand250030004500We have to develop a…

Q: Find all zeros of the following polynomial. Be sure to find the appropriate number of solutions…

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Q: (b) Show that if h(1) = h(2) = 0, then the term O(e) in this expansion vanishes if y'(x) satisfies…

A: To show that the term   in the expansion vanishes under the given conditions, let's consider the…

Q: Consider the following. 49 7 -7-y ſªº √√ √¹¯³ ƒ(x, y, z)dzdydx Rewrite this integral as an…

A: To rewrite this integral as an equivalent iterated integral in the five other orders, we have to…

Q: Let f, g: R → R be continuous at a point c, and let h(x) = sup{f(x), g(x)} for x € R. Show that h(x)…

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Q: Compute the Matrix Function e A where 0 A = [ i and use 0-2 O 3 Ceyley hamilton theory 1

A: (.)  Given matrix is,              (.) Diagonalization: An square matrix  is said to be…

Q: 3. Let A CR, BC Rm. If the Cartesian product A x B C Rn+m is compact, show that A and B are compact.

A: To show that A and B are compact, you can use the fact that the Cartesian product of compact sets is…

Q: Suppose A is a 2 x 2 real matrix that has two eigenvalues A₁ and ₂, and X₁ is not equal to X₂.…

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Q: Use Newton's method to find an approximate answer to the following question. 5 Where are the…

A: Given:The given function is:To find:approximate where the inflection points are located by using…

Q: Solve the given initial value problem. (elimination style) dx/dt = 4x + y - e^4t, where x(0) = 1;…

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Q: 3. Compute (3), (i), (7) and confirm Pascal's Identity for these quantities

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Q: 2. In a vector space V with inner product (,), the vectors u and v are orthogonal and ||u|| = 3 and…

A: Given thatIn a vector space V with inner product , the vectors u and v are orthogonal and We have to…

Q: A sequence (n)-1 is said to oscillate if lim inf n<lim supen and both lim inf n and lim sup In are…

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Q: 21. Let G be an abelian group with subgroup H. Let G/H be the set of cosets of H in G. Define…

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Q: [1-12] 2 1

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Activity 10.8.3. Use the method of Lagrange multipliers to find the dimensions of the least…

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Q: Compute f, and f, for the following functions. (a) f(x, y) = x² + 3xy + y −1 (b) f(x,y) = x²e³

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Q: timate the areas under the curve by computing the left Riemann sum Lg. AM 1 -1,8

A: In this question, we will find the left Riemann sums.

Q: 56. The region bounded by the graph of f(x) = 3x² + 1 and the x-axis on the interval [-1, 1].

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Lou's Bakery has established that JIT should be used for chocolate chips due to the high probability…

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Q: Find the charge q(t) on the capacitor and the current i(t) in the given LRC-series circuit. L = 1 h,…

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Q: Give examples of functions f and g such that f and g do not have limits at a point c, but such that…

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Q: Let V be the vector space of symmetric 2 x 2 matrices and W be the subspace a. Find a nonzero…

A: Let   be the  vector  space  of   symmetric matrices.Suppose  that Then,               a) Choose .…

Q: Evaluate the definite integral 꽁 +1 라 +1 24 ㅠ - 1 -3 ○리-1 24 ○ 1+1+C 얘 16 2 x² + cos(x) dx.

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Q: Find general solutions for the following differential equations (a) x²y" - xy + y = 2xlnx + 10

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Q: Prove that √12 is irrational using the Fundamental Theorem of Arithmetic.

A: Given : Fundamental Theorem of Arithmetic .To show:  is irrational .

Q: Consider the functions C: R → R and S: R → R defined by C(x) = Σ n=0 (-1)" x ² (2n)! and S (x) = 00…

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Q: The graph of a particle's velocity v(t), is shown below. Time is in seconds, and velocity is in m/s.…

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Q: 12. A circular flowerbed is 6 meters in diameter and has a circular sidewalk around it 1 m wide.…

A: A circular flowerbed is 6 meters in diameter and has a circular sidewalk around it 1 m wide. We have…

Q: Determine the following using the picture below: a. Does the limit as x tends to 3 exist? b. State…

A: Determine the following using the picture below:a. Does the limit as x tends to 3 exist?b. State…