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Q: - 2ry? = 0, y(0) = -1. The interval I of definition os (D) (-∞0, 0).

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Q: Ex , Prx , fy, fyy, Pxy, fyx F(X, y) = %3D x +y

A: Given: f(x,y)=1x+y

Q: Q4) Find the deviva tives of the follocoing (9) y = ( In xe) %3D (b) Sec ( ²+1 %3D

A: Part A -  We can observe that the power in the expression on the right-hand side contains the…

Q: What is

A: Rational Numbers: A real number has the shape pq, wherever p and letter of the alphabet area unit…

Q: Apply Uptimal obtain y, y₂₁ and y for the pr 3

A: given y'=t+2y h=0.1 and y0=1 to find the y1,y2,y3 proceed as follows Apply Runga Kutta 2 order…

Q: x=In i y=r2, find y " when For x=0• O 8 O 4 O 16 O 2

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Q: Let f(r, y) = (3 – y)". Then %3D drdy drðydr

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Q: dz where C is the bo + 6)

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Q: dy(x) z = dr ving statements are false? ive of y with respect to r

A: The value is given as, z=dyxdx. The equation given follows , z is the derivative of y with respect…

Q: (a) Find x, y el such that x+y || x || .. = 1 = || y || = || ** ||**y. ∞o 2

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Q: 2-Which ok the allawing is Tategsal egral domain? and solve them. ZXZ, ZxZ4, IR x Zz x Zu.

A: Integral domain:A commutative ring R with unity and without zero divisor is called an integral…

Q: most consiolera Hon when subiects? Whet is he Impor tont designing on humen

A: In a county, people are very important other than living beings. The human population plays an…

Q: The total revenue and total cost (both in dollars) for selling q Objects are given by TR(q) 800g –…

A: when a function is increasing its derivate is >0 but when its decreasing its <0

Q: Let f (x, y) = 9e2xy what is fryx (x,y) =? %3D

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Q: Evaluate dt 13. 1 - sec t

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Q: Find a linear transformation T:

A: Consider the provided information, T11=23   and T1-1=05 Find a linear transformation T. We can put…

Q: Use the Runge-Kutta 4th order method to find the values of y where x is given that y = 1 when x = 0…

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Q: Let y = eka, where k is constant. The values of k .1, –3 that make y" – y – 2y = 0, are %3D :Select…

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Q: whot is the eq ualion ot thl taney @art lime to the fumctionfra fcx) = x+ 5x-2 at the point (-6;4)

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Q: Let f(z,y) = z* + y° – 2r° - 4y be given. Which of the following statements is correct? %3D

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Q: c) Show thiat det a q² -k-1)(61)-) I <a<b %3D

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Q: Let f(x ,y, z) = x²yª + z³ and x = 4s?, y = 2st?, and z = 3s?t. %3D %3D

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Q: af axdy of f (x, y) = xy(x+y — 1) — x² Find-

A: The given function is: fx,y=xyx+y-1+x2   As we know that; The Power Law: ddxxn=nxn-1 The Product…

Q: Find the real numbers x,y,z,t if -3x +y+ zt = 0 3x + y(t – 1) – z(t+ 1) = 0 3x +y+ zt =t+2 - 3x +…

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Q: Let f(z) = x? + iy² where x and y are the real and imaginary parts, respectively of z and C is a…

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Q: Let f (x,y) = e**ytan (x + y), find дудх

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Q: The range of f(x,y) = 2 - x2 + 4y² is : O [0,2] O xy-plane Joo+7] O

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Q: Frd he e of teepkan in the at quectert baurded on he let ty he ydx, bebw by tte carve x- boletby…

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Q: Write a in the form a = arT + aN N at t-0 for R(t) = t2i + %3D (t+r) + ( -r°*

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Q: Express the following functious by Cartesian equetion r=4 tano seca r= 4 CSCO 2 t=l+2rcosa

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Q: sWhat are the points of discontinuity? (x+1Xx-5) y3D *+4x+3 Ox-3, x--1 Ox--3, x=-1 Ox=5 Ox=5,x=-1

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Q: 27. || x sec?y dA, R={(x, y) | 0 < x< 2,0 < y< /4} R 28. || (y + xy-2) dA, R={(x, y) | 0< x < 2, 1 <…

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Q: 2. Evaluate (3xy+iy²)dz along the straight line joining z = i and z = 2 – i.

A: Given the Integral, ∫i2-i(3xy+iy2)dz We, know that z=x+iy ⇒dz=dx+idy, When z=i    ⇒x=0 and y=1  When…

Q: If z=x+iy where x and y are real, find the real and imaginary parts of:- Z+1

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Q: O The madices of cervadere af r= éat any poind Y, is (@) r?VTt (b) rvite? (C) Vitaž (d)

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Q: The domain of f(x,y) = In ry is points (x, y) in the first quadrant. Select one: O True O False

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Q: 6e? Evaluate dz by residue theorem, 9z4 + 45z3 where C'is the contour z = 2

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Q: ニメ Find the eg uaton (x) 4a| %3D 3tan x when fo f the tor

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Q: is given by (X – Y) ± Z V where Z. is a real number such that PİZ > 7.) 4 for Z ~ N(0, ).

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Q: What is the degree of f (x, y) = 2y + Væ² + y? ? O 1 O 2 O 1/2

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Q: Let f(r, y) = 2ry +3x?y2, then fry

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Q: What would allow you to prove AQRS = AXYZ by HL? R4 A ZQS = ZXZ B ZR ZY CZQ ZX D ZQ and X are right…

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Q: where: %3D Solue ulX, o)=2 X •a u (0,t)=o 1 ノ

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Q: What is the degree of f(x, y) = 2y + √x² + y² ? 01 00 O 1/2

A: what is the degree of f(x,y)=2y+x2+y2 degree: it is the highest power of function

Q: Let z = x(1 – i) + 8(-2+ i), where x is a real number. If z? is a negative real %3D number, what is…

A: Given, z=x(1-i)+8(-2+i) and z2 is a negative real  number. We have to find the value of x

Q: Find dy/dr if y = r In(x). Answer:

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Q: The domain of f(r,y) = In xy is points (z, y) in the first quadrant. Select one: O True O False

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Q: Let (-) - {. S 8x², x 9 Find the values of a and b so that f will be differentiable at x = 9. а i b…

A: For differentiable function, left hand derivative is equal to right hand derivative

Q: The formula for the midpoint of (x1, y1) and (x2, Y2) is: M =| O True O False

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Q: Find the are length of f(r) = (r + 3)2 from r = 0 to x = c in terms of c. %3D 2/3

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!