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Q: * t/3 Evaluate the integral S'(y cos x – 3) dydx. S x -

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Q: Determine weather the statement is true of false. Explain your answer.

A: Consider the given differential equation dydx=1x2+1 Use separation of the variable method to find…

Q: Let g(t) be piecewise continuous on [0, ∞) and of exponential order, use the convolution theorem to…

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Q: 1 1-xl-x²-y? Evaluate the integral S S [dz dx dy 0 0 0

A: We will evaluate the given integral in this question.

Q: 22 dt at x = 4. ind the linearization of f(x) = 7 - 4 +t

A: Consider the given function fx=7-∫7x+3224+tdt

Q: 2 Let f (x) = x on [0, 1] Calculate x dx and x dx by dissecting O, I] oaual narts and hence show…

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Q: (a) Let X have the following pdf : S2(x - 1) 1<z<2 S(2) = elsewhere. Compute E(X'), E(2X-1)

A: As per our guidelines we are suppose to answer first question.

Q: 1. Show (in terms of e – 8) that a function f : R³ → R defined by f (x, y, z) = (2x + 3y + 4z) is…

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Q: What type of DE is the following? xydx + (x2 – 3y)dy=0 O Bernoulli in x Bernoulli in y O Linear in x…

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Q: Find the Jeneral integoation of each of B ernoulli's differentialequations (1-x*) y' -xy = aXy

A: Given differential equation is: (1-x2)y'-xy=9xy2 Rewrite given differential equation is:…

Q: (c) f(x,u, v) = – log(uv - x" x) on dom f = {(x,u, v) | uv > x² x, u, v > 0}.

A: C.

Q: 4.78 Compute P(u – 20 < X < µ + 20), where X has the density function f (x) = { 6x(1 – x), 0<x< 1,…

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Q: hoaph fumeten nd be fure at label aut least thne f (u) : Su

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Q: Question 8 Show using e, 8 methods that the functions f (x) = 1 and g (x) = sin r %3D 1+ x2 are…

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Q: (a) Evaluate the integral ſ x e2x çdx (2x+1)²

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Q: In(x) Evaluate the iterated integral: dx dy xy 1. 1.

A: For solving this double integral, first we have to integrate w. r. t x , while doing so we have to…

Q: 3. Evaluate the iterates integral: SL(x-y) dy dx

A: We have to solve

Q: 2. If A = f+ g,+ hy s.t f(x.y.z) = e2x, g(x.y.z) = xcosy, h(x. y. z) = log 2z then div A %3D %3D

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Q: 1. Show (in terms of e- 6) that a function f : R + R defined by f(1. y. 2) = (2x + 3y + 42) is…

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Q: dz If z = xy ln(x + ythen ду MC8.2.pdf I y х| In(x + у) + x + y У In(x + у) + x + y O y(1 + In x +…

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Q: c) Suppose fand g are integrable and that S(x)dx = 4 , [ f(x)dx= 6 , [ g(x)dx= -2. Find the…

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Q: 4. ·| cotl t• dt 0. lim limitinin değeri kaçtır? n In(x + 1) a) 3 b) 1 c) O 2 d) 4 Boş bırak

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Q: #3. Suppose that h(x) is integrable and that ,h(x)dx=1 and S,h(t)dt = 6. Find a. Sh(x)dx b. –…

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Q: 1. Show (in terms of e – 8) that a function f : R³ → R defined by f (x, y, z) = (2x + 3y + 4z) is…

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Q: HW.8. Use farseval's theorem to find if f(t)=A e-alti Ans: A?

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Q: 60. Is there a value of b that will make Sx + b, x<0 (cos x, x20 continuous at x= 0? Differentiable…

A: A function is continuous at x=c, if LHL at c=f(c)=RHL at climx→c-f(x)=f(c)=limx→c+f(x) A function is…

Q: 1-cos(z) if 0 < z < ™ X has PDF f(1) = %3D .0 otherwise Find the probability P(0.64 < X < 2.76).

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Q: Find a continuous function c:t→ Ct, 0 sts1, to 1 minimizec:)os:s14 Sociat dx subject to = Xt + Ct,…

A: Given, minimizeCt0≤t≤114∫01ct4dt Now, integrating the given integral we get, 14Ct4∫01dt=14Ct4t...1

Q: 1) Estimate In(1.1) using a linear approximation. 2) Let y = ln(x). Compute dy when x = e and dx =…

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Q: In z 25 If the triple integral So" Sõ So™² (xe¯y) dydx dz Find the upper limit value E.

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Q: 11:32 E O 1 Evaluating the integral f In(x)dx, where x> 0 yields:

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Q: 2. Suppose that h(x) is a continuous function, h(-1/4) = 1/2, h(7/4) = 1 and h(2)dx = 2. Evaluate…

A: Here, given that h-π4=12, hπ4=1 &amp; ∫-11h(x)dx=2...(1)

Q: Integrate the fuackion f=g regian bonndel by y the en6* y-o ver

A: The function is fx=xyThe region is bounded by y=x, y=6-x, y=0

Q: 2. Evaluate the given integral. S1– x if æ > 1 | 2² – 1 if a <1 f(x) dx, where f(x)

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Q: 8. Let f(x, y) = cos(y – x) and r(t) = (e', e2t). Find if (r(t)) at t = ln(3).

A: The solution is given as

Q: 3 5. Evaluate the iterated integral: S x(x² + y)'/² dx dy.

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Q: 1+ax' Let f(x) = cos(x) In | be integrable on If | f(x)dx = 0 where a and b are real 1+ bx a+b…

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Q: 25 3. In r If the triple integral fo So So (xe") dydr dz Find the upper limit value E.

A: We have to find the value of E.

Q: 2. Set up an integral to find the exact length of the curve defined by 1 f(x) = 1 In r 2 - 4* where…

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Q: If x = k (1+ e*) dy _ x² + x°ew/ s° +2yeb/a} prove that dx 2xyely/x}

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Q: Compute the general antiderivative S a"-1 cos(x")dx COS where n > 1 is an integer greater than 1.

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Q: A:= {(x, y) € R² :1< log(x) < 2}. = {(x, y, z) E R³: sin(xy² + «/2) · cos(z) = 1} . (a) Decide…

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Q: Assume x and y are functions of t. Evaluate dy / dt for 4xey = 8 - ln 64 + 6ln x, with the…

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Q: Which of the following functions has a maximum y value of 4 Oy= 4cos x y= cos 4x Oy= cos x + 4 Oy=…

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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: Show that there exist constants 0 < A < B <∞ such that, for every y, z ER with A В 1 dx < ly – z|3…

A: We need to prove that there exist positive and finite constants A≤B such that, Ay-z13≤∫ℝ1x-y23…

Q: Suppose f(0) = 5, f' (0) = 5, f(1) = 4, f'(1) = 6, g(1) = 8, gʻ(1) = -3, and H(x) = f(ln(x)) +…

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