dy 1- IF y = cos(3 cos 2x) find dx 2- IF y = (x3 + 3)(2x* – x) find y" dy 3- IF y = sin x find when (x =;) dx %3D

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Q: 22. Let P be an idempotent matrix. Show that the only eigenvalues of P are A = 0 and A = 1. [Hint: S...

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Q: If the geometric sequence is {50, -10, 2, ..} (a) the 7th term is . Round answer to four decimal pla...

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Q: 4. Define two ordered bases B = and C = on R³. (i) Find PB-. (ii) Find numbers a, b, c satisfying = ...

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Q: (sin(æ) + 2 cos(y)) dy ^ dz + (zổ – y cos(x)) dz A dæ + 11xyz dx ^ dy. Find dw. dw dx ^ dy ^ dz

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Q: 1. Find the general solution for each of the following Cauchy-Euler equations. (a) x²y"(x) + 3xy'(x)...

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Q: 8. Find the sum of all integers between 20 and 29, including these.

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Q: cos(2) dz c (z – n)(z – 27)3' 7. Evaluate where C : z– 27 = 27 described once in the clockwise direc...

A: Q7 asked and answered.

Q: Find a formula for A", given tha

A: Given, A=-1624-1826,  P=4131,  D=2008

Q: 1.) Draw a line AM (which is of line PY) to form angle PAM orien of line PY. Hint: Point M should be...

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want...

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A: Introduction: The Laplace transform of the function F(s)=1s-a, s>a is given by, f(t)=eat

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Q: c. In what quadrant does 5.5 e3.5i rad lies?

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Q: Exercise 8.7.9. In each case, use Definition 8.7.7 to determine whether g is an inverse of f. (a) f:...

A: 1. Given  f(x) = 9x - 6 g(y) = y+69 So fgy = 9y+69 - 6 = yandgfx = 9x - 6 + 69  =  x Hence g is a in...

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Q: Let x be a real number. Prove by contrapositive that if x + 5x = 40, then x < 3.

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Q: 27. Find examples of (2 × 2) matrices A and B such that det (A + B) + det(A) + det(B).

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Q: Find the area of the region bounded by the graph of

A: GIven,          f(x)=abx-x2, and  g(x)=cx Here,        a = 4, b =8, and c = 5

Q: Find the given inverse transform (1) c{ (i) L-1 s2 + 6s + 1 1 1 (ii) L-1 |(s – 1)3 ™ s² + 2s – 8

A: The Laplace transform of a function f(t) is defined as Lf(t)=∫0∞e-stf(t)dt. If F(s) is the Laplace t...

Q: Consider the linear operator L: BC[0, ] → BC[0, 7] defined by Си — и" - 2и is unbounded in the sup n...

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Q: -3 a 1 f B -9 1 3 is the adjoint matrix of a 3 2 -4 0 then the value of a is

A: Given, B=-3a1-91322-4 B is the adjoint matrix of 3×3 matrix of order A. 

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A: In this question, the concept of a truth table is applied. Truth Table In logic, a truth table is a ...

Q: Let x be a real number. Prove by contrapositive that if x + 5x = 40, then x < 3.

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Q: Prove that 3 | 22n+1 +1 for all natural numbers n.

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want...

Q: In Exercises 12–17, find the eigenvalues and the eigen- vectors for the given matrix. Is the matrix ...

A: Given matrix 121012001 we have to find eignvalue and eigenvector 

Q: и" + 7u 3D 0

A: Given differential equation u''+7u=0we have to find general solution

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Q: z eaz dz 1 6. Evaluate 2ni is a real constant. where C : |z| = 2 described once in the anticlockwise...

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Q: Jo (1+ For which valMcs af v does twe tamproper inbeg

A: Ghh

Q: Prove that the only idempotent elements in an integral domain R with unity are 0 and 1.

A: Proof. Let x ∈ R be idempotent, 

Q: Suppose that A = 2i + j, B =i- 4j + k, and Ĉ = j+k. What is Á· (B x Č)? A) A. -2 в) В. -2 k с) С. -1...

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Q: 1. Evaluate the following limits. r+7| b. lim -8- x2 + 7x – 8, x + 8

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Q: 33. Find a linear differential operator (of lowest order) that annihilates the given function: f (x)...

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Q: A container initially contains 11 L of a salt solution. Water flows into the container at a rate of ...

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Q: 1. Evaluate the following limits. r+ Vr* – 3r a. lim - Vr4 + 3x

A: Brief explanation is given below.

Q: 1. Evaluate: e 3z I = dz (e² + e5z)2

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Q: Part 3: Determine whether B is the multiplicative inverse of A. Show your solution. 1 -1 1 -1 B 1 -1

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Q: QUESTION 4 Let G= be a cyclic group of order 20. Find all the elements of order 10 in G.

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Q: 3. If m29=2r+ 5 and m2 8=3x find m28.=

A: Given:m∠9=2x+5m∠8=3xTo find, m∠8

Q: Σ >k· k! = (n + 1)! – 1 k=1 for every positive integer, n

A: We will prove this by principle of mathematical induction.