Use the Mean Value Theorem (MVT) to establish the following inequalities. (a) sin r- sin yl < |ar – y| Vr ER. (b) T < In(1+ x) < r for -1< r < 0 and for a> 0.

Q: Find the absalute maxima and minima for the function 48xy -32 x 4 yen thhe rectangulaK plate boundad…

A: We have to find the absolute maxima and minima of f(x,y).

Q: Question 19 Find the solution. y3 y (0) = 1 dy dx 1-2xy2 A yx²– In lxl=0 B -xy²+ In Ixl=0 © 2ry2+ In…

A: Given differential equation is dydx=y31−2xy2......1 and y0=1. We have to find the solution of the…

Q: Use the method of variation of parameters to find a particular 32e*/2 that does solution of the…

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Q: 1. Evaluate dz 22 where (a) C = C (1); (a) C = C† (1).

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Q: 4. Determine the number of zeros of the function f(2) = 2zª – 2iz³ + z² + 2iz – 1 - in the upper…

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Q: undetermint coedticients 11 ON-4y = G²-3) sin x

A: The given problem is to solve the given non homogeneous differential equation using method of…

Q: Problem 6. Consider the plane, X, in R given by the vector equation: x(s, t) = (1, –1,2) + s(1,0, 1)…

A: The complete solution is in given below

Q: Example 6-44. Show that eitr = 1 + (eit – 1) x(1) + (e# – 1)2 ) + + (eit – 1y. where x =x (x – 1) (r…

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Q: \Question No.2 Find f(1), S(2), S(3), and f(4) if f (n) is defined recur- sively by f(0) = 1 and for…

A: Multiple :    (a) We have , given a recursive formula ,  fn+1 = f(n) + 2 Also , f(0) = 1 For , n = 0…

Q: 3 Let R be the region inside the curve C :r = 1+cos 0 and to the right of the line € : r = - sec 0.…

A: Given R be the inside region between the curveC : r=1+cosθ and the right line l : r=34secθ. (a) We…

Q: 3. Let f(z) = 1-z and y(t) = t+it for t E-1,1). (a) Sketch the image of the curve y. (b) Evaluate…

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Q: How many positive integers not exceeding 3000 are divisible by exactly two of 4, 10, 12? (Steps…

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Q: (n+1)x*! – x* . cos ((n+1)x) dx, where n is 4

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Q: 7.(This one is a gift) Consider a homogeneous differential equation, p(x, y) dx + q(x, y) dy = 0,…

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Q: Find graphically approximate value of the root of the equation an 3 – x = e* - 1.

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Q: [1 0 17 C=0 1 1: 0 1 0 [1 1 1 D=0 0 1- 10 0 Го A = Let B = [1 07 1 0 0 1] E-1 0 1 0 10 10 1 1 F- 0 0…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2. For n > 1, let sn denote the number of n-bit strings that do not contain the pattern 001. (1).…

A: The complete solution is in given below

Q: 3. Use De Moivre's Theorem to solve for the roots of : a® – 1 - j1 = 0 O A. 1 cjs (T/24 + rtk) ; k =…

A: Introduction: DeMoivre's theorem is a significant theorem in complex analysis. It is used to find…

Q: Perform Gauss-Seidel Method to the given system of linear equations. using x, = 0, continue…

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Q: 6. We consider any holomorphic function f(2) : D → C \ {0}. An function g : N→ C is called a branch…

A: Fix a point p∈Ω, and consider gp a solution of  egp=fp The solution is always exits as fp≠0. let…

Q: The regions A, B, and C in the figure below are bounded by the graph of the function f and the…

A: The average value of the function

Q: Question 23 Find the solution. 2y dx = (x2-1)(dx - dy) %3D A (y-1)y (x+1)(cx + y- 2lnly+1|) B (x-1)x…

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Q: Let R be the region inside the curve C:r=1+cos0 and to the right of the line € : r = - sec 0. 2.1.…

A: Since you have posted a question with multiple subparts, we will solve first three sub parts for…

Q: Classify the point (37, 7) for f(x, y) = sin(x + y) – sin(x – y) by using Second derivative test if…

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Q: ×- -X+ し SY STEM = ニ メ=ーと 2) a tbt ーt ニ t d山

A: This is a problem of linear transformation.

Q: Find the general solution of the equation: у" - у' - бу %3D еxp(-x) - 7 сos х

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Q: Q8. a) Determine an algebraic expression that represents instantaneous rate of change at the point x…

A: Instenatinueous rate of change of the function at point

Q: A silo consists of a right circular cylinder surmounted by a hemisphere. Find the most economical…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs…

Q: In practice, when comparing two means using small samples, when would you recommend assuming equal…

A: Option (D) is the correct answer.

Q: 0ダュクー = cos y

A: Note:- Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 1. Find the determinants of the following matrices using Laplace Expansion and Triangular matrices…

A: find the determinants of the following matrices using laplace expansion and triangular matrices. (i)…

Q: (a) Obtain the truth table of the function. (b) Draw the logic diagram using the original Boolean…

A: As per the company rule, we are supposed to solve the first three subparts of a multi-parts problem.…

Q: 3. Compute log r 1+x²

A: Given, Integral = ∫0∞log x1+x2dx To find - Value of given integral.

Q: Question 6 Find the solution. dy 2y dx Ay = x(x+c) By = x³(x+c)3 y = x²(x+c)2 Dy = x2(x-c)-2

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Q: The system of linear equations: x1 + 2x2 + 3x3 = 2 x1 – x2 + 2x3 = 1 Select one: O a. None of the…

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Q: Suppose the region R is bounded by y = 0, y = x, and x = 1. Evaluate: 4.x2 dA =??? 1+x4 R 2.0 1.5 dy…

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Q: Find the differential of the function y = x- sin x.

A: Given: y=x2-sinx

Q: rections: Henry thinks that X = 22 . Is he correct? Follow the checklist below to help determin…

A: find the values as follows sin 38°=0.61566 cos 38°=0.78801 tan 38°=0.78128

Q: 10. Assume / || m. Find the value of x. (r+72)° (3x) O 24 O 20 O 27 O 18

A: Solution :  Given angles  (x+72)° , (3x)°

Q: An architecture student is designing a curved building and evaluating the volume enclosed vithin the…

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Q: n! (j) Sn n'

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Q: a b -b a Let V be the set of all 2 x 2 matrices of the form where a and b are real numbers. (a) Show…

A: Let V be the set of all 2×2 matrices of the form ab−ba where a and b are real numbers. That is…

Q: 1. Using Three point Forward difference, Backward difference, Central difference formula numerical…

A: We can solve this using given details and used formula

Q: 6. Are these triangles congruent and if, so, for what reason? O Yes, SSS O Yes, SAS O Not congruent…

A: We want to find the both triangles are congruent or not.

Q: Approximate the arc length of the curve y = x over the interval [1, 2] using the trapezoidal rule…

A: Introduction: The length of arc of a given curve over a given interval is another important…

Q: ad been his friends and fellow Royalists, Sir Charles Lu pom, however, he was one day handed the…

A: Mark the third letter after each punctuation as follows Write the letters…

Q: 1+a 1 1 1 1+b 1.1 1 + 1 Prove that 1 = abcd 1+ 1 + a 1+c 1 1 1 1 1+d

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Q: (1) Consider the following differential equation, with time domainte (0,1): Sy = ( -1)y. Lu0) = 1.…

A: Solution is in given below

Q: 1. If there are five types of batteries which are AAA, AA, C, D, and 9-volt and you want to put…

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Q: 1. Using Three point Forward difference, Backward difference, Central difference formula numerical…

A: To use three point Forward difference, Backward difference, Central difference formula to find…