Prove that zero is a root for the equation ax' + bx² +cx+d = 0 if and only if d = 0. What can you see if c=d =0?

Q: Find the firct derivatioves of the follwing: - 3 ) y= 3x-x -2 4) y: Jerx 2) y: Ji-7x 5) y = 2メ-3

A: ddxxn=nxn-1 ddxu(x)v(x)=v(x)ddx(u(x))-u(x)ddx(v(x))v(x)2

Q: what is the equation of the tangent line to xy-3y^2=1 at the point (4,1) Express numbers in eaxact…

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Q: 4) Find linear ditterental equation with costnt y-ac'+cadk Lomageneas coetfients whose general…

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Q: 6. Parallel to the line Y = = -}(x – 100) – 99, 3 4 passing through (1, 3)

A: Given query is to find the equation of the line passing through (1,3) and parallel to the line…

Q: 2) Use the false position method to find a root of the equation ex + 2-x+ 2cos x = 6 in the interval…

A: Solution :_

Q: integral -{cay,a> 91-) Evoluate te nplhas)ss - 24x<0, Ocyc1, -16241} . where

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Q: Use the Existence and Uniquness Theorem to verify, with initial value (-2,-1): y' = xy2

A: Consider the differential equation y'=xy2 with initial condition -2,-1 Compare the differential…

Q: (5) Find the particular solution passing through the point (1,8) How does this solution behave as t…

A: Sol

Q: A number of the form iy is called pure imaginary

A: A number of the form z = x + iy is known as complex number, where x is real part and y is imaginary…

Q: Boundany condition

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

Q: Form the polynomial equation with integral coefficients whose only roots are given. 2,-1,1

A: Given roots are 2,-1,1 Now we have to find the equation of polynomial with

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: Calculate the real root of f(x)=x^3-2x^2-2x-1.9 with the first iteration of Newton-Raphson method.…

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Q: Suppose that 3x² - y² = 1² and y=tsin 0. Find (3). = sin 0 y (1) ¹ (2) and (2) 0 X X

A: Let's find partial derivative of given two equation.

Q: the rocket exploded at the peak of the projectile, part I falls at distance less than d to the…

A: In the given question, the concept of Centre of mass is applied. Centre of Mass The centre of mass…

Q: id I prove this qa is not to zero correctly? Please look over my proof and qa is not equa

A: Proof by contradiction:  Argument by contradiction is a type of proof in logic and mathematics that…

Q: Suppose that your first guess is lucky, in the sense that x0 is a root of ƒ(x) = 0. Assuming that…

A: Newton’s method is performed to obtain the approximations using the following formula.

Q: Usin IVT how do you show this equation has a root. On the interval (0,2)

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Q: A stretched string of length 20 cm is set oscillating by displacing it midpoint from the rest…

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Q: Use the false position method to find a root of the equation (e power x) +(2 power −x) + 2cos x = 6…

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Q: FIND THE REAL ROOT OF X.EXP(X) = COSX BY SECANT ITERATIVE METHOD CORRECT UPTO 4 DECIMAL PLACES.

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Q: Find the point (s) on x = 3 - y2 that are closest to point A = (1,0).

A: Given: x = 3 - y2 and point A = (1, 0)

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: What happens in Newton’s Method if your initial guess happens to be a zero of f ?

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Q: Sec-S 2 1 TanOLO

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Q: 3- Find the smallest positive root of x -e*=0, correct to three decimal places, using (method of…

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Q: Find the root between (2,3) of x3+ - 2x - 5 = 0, by using regular falsi method correct to three…

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Q: y = In(x-2) ex+1

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Q: If Z= sinh () x- show that:

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Q: uxiliary equation of + by = 0 are re tion of the different

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Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: Solve MXVN at (1,1-1) When M = (2yz)i – (x²y)j + (xz²)k and N = 2x²yz³ Show the graph after it.

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Q: The 2nd approximation to the real root of the equation x³ – x² – 1 in the interval [1, 2] using…

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Q: The Newton-Raphson method is used to find the roots of the equation: Ax) = x – cosTX ; Osxs1 If the…

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Q: How can we use the general definition to prove the theorems?

A: Query- How can we use the general definition to prove the theorems. Answer- A theorem is a statement…

Q: Calculate ∞0 1 e -3t √t - dt

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Q: : Find a root of x- 0.5 – 2-2x = 0 by using Newton-Raphson method correct to 4 decimals so that the…

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Q: Find an interval of length 1/4in [1, 2] containing a root of the equation x^7 + 3x − 10 = 0.

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Q: 3- Find the smallest positive root of x-e=0, correct to three decimal places, using (method of False…

A: False Position Method : An algorithm for finding roots which retains that prior estimate for which…

Q: Explain theorem of Wronskians of Solutions?

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

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: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

Q: Find the real root of the equation x^5-x^4-x^3-1=0, Which lies between 1.4 and 1.5. correct to four…

A: The given equation is: x5-x4-x3-1=0

Q: Express the first four cumulants in terms of central moments.

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Q: Prove sech 2  x =1 - tanh  2x

A: we have to prove: sech 2  x =1 - tanh  2x

Q: Use Newton's method to estimate the one real solution of x° + 3x + 1 = 0. Start with x, = 0 and then…

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Q: Find the positive root of the equation x + 2x2 + 10x - 20 in the interval [1,2] using Regula Falsi…

A: Let, the given function be: f(x)=x3+2x2+10x-20 And, the formula of the method is:…

Q: sech2(In x)

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Q: Find the orthogonal trajectories of the functen X + ce-X which is . passing Thieugh (-2.0)

A: We need to find the orthogonal trajectories of the function y=x+ce-x, which is passing through (-2,…