Prove that the equation * + + = 1 has no solutions in positive integers x , Y, Z.

Q: find the genecol solution of Cauchy EuLer equation

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Q: 2. Prove: cot2x - csc²x = -1 %3D

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Q: Determine the solution set of the matric Ax=0 where A= 1 2 3 2 3 4

A: Given the system of equation is AX=0 where

Q: Boundany condition

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

Q: Compute Ax by dot product. 2 10 1 2 1 0 0 1 0 0 1 2 1 2 1 1 2

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Q: Find the indefinite integral: 10sin 3x - 15 cos 2x + 6 e5x + C O 90sin 3x -60 cos 2x + 150 e5x + C…

A: 30∫cos3x+sin2x+e5xdx=30· ∫cos3xdx+∫sin2xdx+∫ e5xdx=30·…

Q: 2. Show that c(x, t) = solves 1 ac(x, t) 2 ax ac(x, 1) ar

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Q: The integration expression Jsin(3In(x)+ 4)cos(3In(x) + 4)dx must be transformed into using suitable…

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Q: 1. The first approximation of the root of xlogx - 1.2 = 0 in [2,3], by Regula Falsi method (False…

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Q: | In(vE + 5)dt

A: Given: I=∫lnt+5dt  ……1

Q: 7) Solve for x: In(x + 3) = In(2x) %3D

A: The given equation is lnx+3=ln2x.

Q: Prove that the equation ! + = 1 has no solutions in positive integers æ, y, z.

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Q: 12 Integrate: ,V4 - z² + dr

A: The given function is 4-x2+x7+24-x2 We have to integrate this function over the interval -2, 2

Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the indefinite integral: O 10sin 3x - 20 cos 2x +6 e5x + C 90sin 3x 60 cos 2x + 150 e5x + C…

A: The objective is to find the indefinite integral.

Q: 2. Find the desivative ofy= Binx

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Q: Show that the solution (if exists) is unique:

A: Given, u =6x + 4y +2 on {x² + 4y² <1} u(x, y) = x+2y+y²-4xy²-8y³ on {²+4y²=1} Using maximum…

Q: Show that |1 - (x, + x,) - (x, + x,) X,*z = (x, – ,) (x, – y2) (x2- ,)(x2 - 2) 1 -(), + x2) 1 - (y,+…

A: See the attachment

Q: Show that - In(x – V - 1) = In(x + Vr – 1)

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Q: 6. Prove that 1 cosh(tanhx) : -1 <x < 1. V1- 12

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Q: 3) Use the Intermediate Value Theorur to show that there ís a root of the equation Make sure you…

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Q: у" - In x

A: Given: y''=lnx

Q: Verify that (AB)" = BT AT %3D التحق ق 3 2 4 2 1 3 A = 2 1 B =1 2 5 4 2 3 0 2 1

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Q: If x,y,z are real numbers satisfying the equation 25 (9x* +y° )+9z²-15(5xy+yz+ 3zx )=0 then prove…

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Q: 6) Prove mathematically that (1 grad = 0.9 deg) %3D

A: Since, this is a multiple question according to the Bartleby Answering rule, only first question is…

Q: Prove using the IVT. ex + In x = 0 has a solution.

A: IVT: If f is continuous on the closed interval [a, b], f(a) ≠ f(b) and k is any number between f(a)…

Q: Solve for DE: separable DE

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Q: Find the number of positive integers less than 1000 that can be expressed as the difference of two…

A: Find the number of positive integers less than 1000 that can be expressed as the difference of two…

Q: 9 In(z² – 1) dz

A: Given: ∫9lnx2-1dx

Q: b) Show that 2x² + 8x + 14 = 2 (x + 2)° +3 by completing the square. Hence, evaluate the integral-…

A: Use integration rules

Q: Show that L₁J - dx x² + 2x + 2 = In(√5-2).

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Q: I need help doing number 7

A: We start solving the given equations simultaneously.

Q: Evaluate the indefinite integral. (7z + 7 71 + -dr Jz² +1

A: Given,          ∫7x+7x2+1dx

Q: Explain theorem of Wronskians of Solutions?

A: To Find : Define the Theorem of Wronskians of solution

Q: 1. Express into parital fraction. Hence evaluate y2 -4 *2-4

A: according to our guidelines we can answer only three subparts, or question and rest can be…

Q: Consider the follow ing LP model: max z = 50x, +100x, X +x, 5 300 | 2x, +x, 5 400 St. X, S 250 X, X,…

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Q: prove that (z(square root 2,+,×)) is integral domain.

A: We have , ℤ2   =  a + b2 / a , b ∈ ℤ We need to show that  , ℤ2 is integral domain. We know that , a…

Q: Show that 1 sech-1x = In x2

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Q: 8-JIE FCx²_ ye, y-z²) =• then Prove that + Xそ 2Z

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Q: The sum of two positive numbers is 16. What is the smallest possible value of the sum of their…

A: Let x and y be the values of the two positive numbers whose sum is 16. Need to minimize the…

Q: How do you integrate z/(z+2) in terms of z?

A: Here, integral is,

Q: "(2) is also analytic, and hence its

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Q: Find ß so that {1, x, 1+ 6x²) on (-1,1) is orthogonal.

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Q: Estimate the In (1.1) and sec (0.1) Using a linear approximation and without using any kind of…

A: f(x)=ln(x) f'(x)=1/x f(1)=ln(1)=0 f'(1)=1/1=1 linear approximation is then L(x)=f(a)+(x-a)f'(a)…

Q: 3)(2x-ズ) ax

A: First I have split the integral in two parts then just use the rule of integral and find the…

Q: (2, Prove that Ž (Pn+ Pn+1) hr 9=U (y+1) 27-²8 (14+ 2x=-1) y

A: What is Legendre Polynomial: Legendre polynomials are a set of complete and orthogonal polynomials…

Q: Find the interval and radius of conv. of In(1 – x²)

A: The power series representation of given function ln1-x2 is given by: ln1-x2=∑n=1∞-x2nn

Q: biz' dt 2

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Q: Prove that: 3-4x² dx 4VIn3

A: The given integral is I=∫0∞3-4x2dx. The idea is to evaluate the above integral using gamma function.…

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.