1 1 Evaluate f dz[ dx [ e dy. бе/3 (бе-б)/3 О бе-6 6/3

Q: (a) Show that y for the given z = e" In x+ xy

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Q: 16. What is the derivative of f (x) = e8x+3? %3D a. f'(x) = e8 b. f'(x) = 3e8x c. f'(x) = 8e d.…

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Q: az xdz + Y- = xy+z. a) If z = xy - xei , show that x- ду

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Compute L(f(t)) 13. L((t+1)²) 1. L(2t) 14. L((t+2)²) 2. L(4t) 15. L(t(t+1)) 3. L(1+2t + t²) 16.…

A: In the given question wen have to find the Laplace transformation of the given functions. here we…

Q: 10. Suppose that f and g are functions of x and y such that dg dy df af ag and dx dy and suppose…

A: The objective of the question is determine the functions f(x,y) & g(x,y) according to the given…

Q: I'(x) p-let dt,

A: Γ 12=2×∫0∞e-u2 du Here, Let's calculate the value of Γ 12, The gamma function is defined as Γ…

Q: het Q be the differential operator defined by Q(y) = y(3) +44 (2) + 5y² + 2y a) golue: Q (y) = 10…

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Q: Vrite a chain rule formula for the following derivative. for z = f(r, s); r = g(t), s = h(t) O dz dr…

A: Given that z=fr, s; r=gt, s=ht We have to write a chain rule formula for the derivative ∂z∂t i.e.…

Q: Verify Young's Theorem y? x2 z = In(2x + y) + +e(x+2y) y

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Q: 3. Find the total differential of z = f(x, y) if z2 - y = (1– 2x)z.

A: Total differential of a function z=fx,y is dz=∂z∂xdx+∂z∂ydy

Q: -2+z) ds over t e point (0, 0, 0)

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Q: 2 =1+ %3D V1+f(t) dt, x 21

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Q: 3 62 what is 13 | f(t) dt? f(x)dx = 3 6.

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Q: (a) x = t* - t + 1, y = t2 Select--- v (b) x = 2 - 2t, y = VE --Select--- v (c) x = sin(2t), y =…

A: Match the graph with their parametric equations.

Q: 6.5.4 Find the PDF of W = X + Y when X and Y have the joint PDF fx,x(z,y) • otherwise.

A: Given: The joint probability density function of the random variables X and Y is provided as:…

Q: 1. re (x, y, z) x). Ly). (z}} - *(*. y, z) . (x)S(x), ly), (z]} (x)E (x, y, z}

A: If x is element then it belong to set And {x} it will be subset of set

Q: Let f(x, y, z) = x°y* + z* and æ = s³t2, y = st, and z = st. (a) Calculate the primary derivatives…

A: Given the functions

Q: 1 F (s) = s (s +1) %3D

A: Given: L-11ss+1

Q: iv) if zy = (x)- then zx + Zy = %3D %3D

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Q: Տhаrⅿа hаѕ еіցht сhіⅼⅾrеո. Βесаսѕе Ѕhаrⅿа іѕ а ցооⅾ fаthеr, hе саո ⅾіѕtіոցսіѕh еасh оf hіѕ сhіⅼⅾrеո.…

A: Given Information: Total number of children = 8 Number of black hats = 4 Number of gold hats = 4

Q: [16.46° At 377 A=-0.25+ j7.9852 Stable -0.1693 -0.50

A: We will discuss how lambda is calculated. Lambda is the eigenvalues. I will show you how lambda is…

Q: 8. Prove that the differential operator M: C² [a,b] → C[a,b] defined by d²u du Mu= 2+3u dx is a…

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Q: 25. What is the particular antiderivative of f(æ) = passing through (4, 1)? 2 3 3 а. У с. у 3 -- b.…

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Q: 7. f(x) = x² In x, f"'(x) 1 8. y = -, y" 1 .f"(q) 9. f(q) = 2g* 10. f(x) = /x, f"(x) 11. f(r) = /9 –…

A: The objective of the question is determine the derivative of the given function "y".

Q: 2 2 If z = f(x, y), where x = s² - t² and y = t² s² and z is differentiable, then - Select one: True…

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Q: (4) Evaluate : + yz') dV if Q= {(x, y,z): x:[-1, 1], y:[3, 4], z:[0, 2]}

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Q: 1. (a) Let f(r,y)- cos(z + 2y). Compute the diectional derivative Df(r,9), where u- (b) Compute ff,…

A: Solve the following

Q: 3. If f(x, y,z)= In *yz +e tar's="), find f,,fy and f. . хуz

A: we have to find the partial derivative

Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: 2.Use the Fundamental Theorem of Calculus Part 1 to find the derivative of the functions 17 yt a)…

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Q: (e) 3x E R, Vy E R, xy > 0. (f) Vx E R, 3y E R, xy > 0. (g) 3x E R, Vy E R, xy > 0.

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Q: 1 So So f(x, y) dydæ A. So SE f(x, y) dædy B. Jo Jo f(x, y) dædy OC. f(r, y) dædy O D. So Si f(x, y)…

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Q: If e**У- ху, then dx x(1- y) A Ax- 1) Ax - 1) B x(y- 1) (1- x) x(y- 1) x(y- 1) (D Ax - 1)

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Q: Given g(z) = In(5z+), the derivative g (z) is. %3D O 42 O 5z +z O 20z +1 O 20z +1 5z4 +z 5z +I 20z+1

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Q: 4.18 Given that g(x) > 0 has the property that 6. show that is a pdf. f(x, y) 2g g(x) dx = 1, (√x² +…

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Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

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Q: B. Let z- ( x-y)e×y (x-y)exy Show: Zxx + zyy + exy Cya-x3)= -z (xy+ 2)

A: Partial derivative of a function z=f(x,y) with respect to x is the derivative of z keeping y…

Q: Suppose that , g(t) dt = v2 g(t) dt 1. g(u) du 2.

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Q: Suppose that f(0) = 1, f(0.5) = 2.5,f(1) = 2, and f(0.25) = f(0.75) = a. Using trapezoidat rule with…

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Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy =yx.

A: Since, yz = zxy

Q: In Exercises 31-42. find dy/dx. 31. y = x4 33. y = Vx 35. у %3D (2х + 5)-12-( 32. y =x-3/5 34. у Vx…

A: 31 . y=x9/4

Q: An M.V.U. is unique in the sense that if T, and T, are M.V.U. estimators for y (0), then T, = T,…

A: Answer: For the given data,

Q: II z= ě Y x - Juv Find dz dv üs ing chein rule.

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Q: Is the function 3Sin26x a special function of the operator d? /dx? ?

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Q: 14. If X has the PDF f(r) = 1/4, -1<r<3, zero elsewhere, find the PDF of Y %3D

A: Given,f(x)=14  ; -1&lt;x&lt;3Y=X2

Q: Verify Young's Theorem z = In(2x + y) y? x2 +e(x+2y) y

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Q: Let g(t) = 2 In 2 In(3t) ). Then the derivative of g is g'(t) = A ( In (3t)) tC, where (In 3 %3D A =…

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Q: 13. Use the chain rule, in Leibniz notation, to find dx dy at the given value of x. а. у %3D Зи? —…

A: We are solving the first three subparts and for the next subparts post the question againand also…

Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy = yx.

A: Assume that x2 = y2 = e and yz = zxy.  Now from  yz = zxy we have  yz-1 = zxy-1z-1y-1 = y-1 x-1 z-1…