1) Prove the following identity: (x + y)² – (x – y)² = 4xy

Q: Given 7(t) =(cosh(1), -sinh(t),t) find 7(t) , Ñ(1), and B(t) and simplify

A: given r→t=coshti^,-sinht j^ , tk^ find  1) T→t , N→t , B→t

Q: 6. Derive each of the following identities. (a) 9ry = 19 + 19y - 19zy (b) fr(t) = 19: tPy Hy+t + 19y…

A: Given qxy¯t=qxt+qyt-qxyt fTxy¯t=qxt pyt μy+t+qyt pxt μx+t qxy¯n|=qxn qyn|+qyn qxn|+qxn| qyn|

Q: Find the general solution of the following ODE. y(4) + 4y" = 0 %3| y = c1 + c2(0)+ c3 cos(O) + C4…

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Q: X 6. Compute the derivative of 21. x²+1° O zx O O x²+1 1-x² (x²+1)² O=1+x² x² +1 ONone of these

A: To find the derivative of given function

Q: Which of the following functions has both a vertical reflection and a horizontal reflection? Of(x) =…

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Q: 14. Evaluate: dt (a) (12 + 1)3/2

A: There are multiple question , as per company policy kindly ask other question separately.

Q: (2xy³+y)dx + (3x²y²+x-2y)dy = 0

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Q: а. Write the following complex function in the form of f (z). f (x, y) = sin x cosh y + i cos x sinh…

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Q: 25. Find a polynomial q e P2(R) such that p(x)(сos TTx) dx p(x)q(x) dx for every p E P2(R).

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Q: Solve the ODE: xy"+2y'-xy Oby using the Frobenius method.

A: Given that ODE: xy''+2y'-xy=0                    .....1 We know that the solution to this ODE is:…

Q: (ii) o S(2xy + z)dx dy dz z=-1 :0 Jx=1

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Q: Evaluate the following complex functions and show your complete solution

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Q: eorem for f(x)

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Q: Calculate A2. Use the trigonometric identity sin?(0) = ÷(1 – cos(20)). 1 A2 (6 sin(0))² do %3D 2 *…

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Q: 1. Find the value of k so that the ODE (y³ + kxy¹ − 2x) dx + (3xy² + 20x²y³)dy = 0..

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Q: 1. a. Let In = exp (nx) sin (exp (x)) dx. By making an appropriate substitution, or otherwise,…

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Q: plot parucul Solu 1. y" +3y' – 4y= sin wx, 2. y" +3y' – 4y = cos wx.

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Q: Use the D-Operator method to solve the following ODE: d y +4y= 2 sin 2.x dx²

A: To obtain the solution, use the following formulae. ddx=Dd2dx2=D2 The particular integral of the…

Q: 1 X 7.(5.3) Evaluate the following. (1) I = (2xy + 3) dx dy 0x2 •π/2 sin y (2) I = (5y + 3x) dx dy 0…

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Q: 1. Show that f(x)= 4 sin(44)+2-x has at least one zero on (-1,0J. %3D

A: we have to show that there exists at least one zero of a function f(x)=4sin(πx2)+2-x on an interval…

Q: Are the following ODE separable, linear, exact? Explain why and demonstrate.  1.…

A: 1. A ordinary differential equation with x and y variables is said to be separable if it is possible…

Q: Solve the following ODE. 3y(x) +4y(x)– 4y"(x) = 8 ,(3)

A: As per Bartleby policy we can only answer one question  Hope you understand

Q: Read each of the two statements carefully. Choose A(if both statements are true), B(if the 1st…

A: Given that, There are two statement following, 1st : xsiny' = (x2 + 1)(y''')4 is a 4th degree ODE.…

Q: a. Show that If z = x+ iy where y 1 b. Evaluate: cosh?(-z) – sinh²(z)

A: Given that z =x+iy For a part , y<0 and we need to prove that | eiz | >1 For b part, we need…

Q: 8. Compute using the trig. substitution S x2 -dx (1–x²)1/2

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Q: 2. a) Solve the following ODE using an appropriate substitution. dy (x – y) = y, y(0) = 2 dx

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