is T Mzxz Mzuz defined by T()=(* ) in vertibla? If so hind Q tb C td its inverse T-l thet is find formula ) ナ ? ?

Q: E. Prove the following: 四- Iz.l 1.

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Q: Use substitutions to waite (In t)at, for seyo (1n ms of と in 0,9 € N, aE IR E IN, a E IR, a#0 where

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Q: Show that Ě = 3xyê+G)+2Ê is R3 and Pind Conservative a potential Ø Rar F. on

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Q: 3. Let F lt) be the antider¡vatPve of f (t) the most general antiderivative of flt>= 8 sec?(t) -92

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Q: If f(z) = cosh(In z“), then f' (7) = %3D %3D Your answer should be rounded to the nearest whole…

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Q: The identity LiS L xyzdzdxdy = "/2 S Sa rsin@cose zdzdrd® x² +y² 1-y² x² +y² is

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Q: Use Euler method to approximate the value of y(0.2), given ay' - by = ce^(kx) + mx , y(0) = 8 with…

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Q: IS T Mene (R) -7 Pz(2) defined by T()= a +2bx+ (C +d )x² In lerti ble ? If so fiad its inverse thet…

A: The answer of given question is given by using some properties of inverse linear transformation.

Q: 11) Simplify the following with both versions of the Fundamental Theorem of Calculus: e2t dt dx…

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Q: In r dy If y , then is cosh z

A: Straightway proceed to differentiate both sides,

Q: we Gtokes theos em. to pvaluate Fel8 whes F=Z?E t y?; +XK and cf1,0,0) (0,1,0) andlogo, i) nr…

A: By using the stokes theorem we have to evaluate ∫CF·dr where F=z2i+y2j+xk and C:1,0,0,0,1,0, and…

Q: 3. If f(x, y, z)= In xyz te(3.0²), find f,,f, and f-· 4

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Q: Use Euler method to approximate the value of y(0.1), given ay' - by = ksin(cx) + mx , y(0) = 12 with…

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Q: * 10% of f we seloct e flems sold during pr obabilitfese Sold by online 9s ea ne turned a day, find…

A: We want to find the following probability

Q: = e. In(16y), then fzz i 30 e5z In(16y) 25 e5z In(16y) 80 esz In(16y) 25 e In(16y)

A: We have to choose the correct answer from the given options according to the given information

Q: The DE : y = e-/Y is seperable Select one: O True O False on

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Q: | 3t In(t)dt

A: We have to solve this question with the help of by parts integration. ∫fgdx=f∫gdx-∫∂f∂x∫gdxdx It is…

Q: Suppose that a) [15x²y; 0<x<y<1 f(x, y) = { 0; otherwise. Compute E(Xy), Var(X) and Var(Y). b)…

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Q: +3 fn d the deivotive of this funckio slape of the tonpent On d the line ot (4,1).

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Q: (10) Without finding T and N, write a(t) in the forma(t) = a-T + ayÑ at t= r(t) =

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Q: Show that the following cosh 3 (0,0) r(3,5) x² y?. (10xdx +6ydy)

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Q: HiW f(x, y) = x +2xy+y² +3x+5y ils Is.5 of (2,-3) (2,-3) al of

A: The detailed solution is as follows below:

Q: Четверг show that the inu of a bounded E tix-oy ne 7 8. use T

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Q: Find k so that dx = ke" + C.

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Q: If z =e* + In(xy) Evaluate- ,and ,at the point (1, 2). Hence, calculate the change in z when x…

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Q: Show that the following ODE is homogeneous then solve it. 2xyy' = x² + y?

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Q: Use Euler method to approximate the value of y(0.2), given ay' - by = kcos(cx) + mx , y(0) = 9 with…

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Q: In evaluating / x(4 – x)ŝdx , if we use the substitution that u = 4 – æ, then what will be the…

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Q: Let f(x, y, 2) = eF tan(x² 2) . Compute fay: (x, Y, z) . Simplify your final answer.

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Q: Evaluate the integral. 2 2 t+ dt 15 OA. 29 О В. 6

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Q: d tanh¬' (In t) = dt 1(1 – (In t)²)

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Q: _Suppose w =+, x = cos² t, y = sin? t, z = ; dw Evaluate at t = 3, by using the Chain Rule dt

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Q: Show that (D+ 3t)D , is not the same as D(D+3t), where D is the differential operator.

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Q: *find te general Souliton hor the XZP +YZq =XM

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Q: (4z + 5)² tan zy= + dr Cos z

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Q: d 1 Prove that: dz (tan¬1 z) = 1+z?

A: Given query is to find the derivative of the expression.

Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

A: Given for the function F(x), F(0)=0 and tangent line to F(x) at x,F(x) has slope xx2+23.

Q: 3 Prove Prive that d tin'u e I du

A: As we now the identity tan2(x) +1=sec2(x)

Q: Use Simpson's Rule with n = 4 to evaluate [² (t³ + t) dt

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Q: Find T, N, B, K and t for r(t) = ti +÷e2'j when t = In 2. 2

A: answer is in next step

Q: H. If g(z) e2*z In , compute g'(r). What techniques should you be using in this %3! case?

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Q: 12 Find the work done for a force F N from æ =2 to x =6 m. x2

A: Here we solve this by taking the integration with given limits

Q: %3D in Fin d E(S an d Var(s)

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Q: for 2xey = 4 – In 1024 + 10ln x, with the conditions dt dx = 8, x=2, y= 0. Assume x and y are…

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

Q: Suppose w=x/y+y/z, where x=e^(4t), y=2+sin⁡(4t), and z=2+cos⁡(3t). A ) Use the chain rule to find…

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Q: 3. Gien that F cxy) = s Can servative find putantial -> functin fo Ě a

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Q: Show that (A − B)T = AT − BT .

A: We have to use the properties of subtraction of matrices and matrix transpose operation. In matrix…

Q: Evculucte the ntegre ree)dt where re =secttleH, tine TNt C 2

A: The given function is

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.