Iff, g e R(x) on [a, b), prove that f? dx + g? dx 2 2 Ifg | dx.

Q: Find a if f(0) = 1, f(;) = }, f(1) = 2 and f(}) = f(}) = a give o f(x)dx = using the composite…

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

Q: Given U(x; y) = In(1+ xy³), show that 2! dxðy

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Q: du ap B) Prove that dx n- dx v2 where u = f(x) and v = f(x).

A: To find  d(u/v) /dx

Q: Let f(x, y, z) = ln () Vxy – sin (cos (zy)) , evaluate ху %3D дх ду

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Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

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Q: Let /:R'R. S(x. y.2) = (e' tan y,x' In y). Compute D(f).

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Q: In evaluating Sx²V1+x dx with u = V1+x, what is dx equal to ? u du a. b. и du c. 2и du 3. d. • 2 и…

A: Since this is a multiple question, according to the Bartleby answering rule, only first question is…

Q: If x = f(u) and v= g(x), what is du dr dx du ○ f'(u)g'(x) ○ f'(u) + g(x) O dv dx + dx du dv du by…

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Q: Given: y = f(u) and u = g(x), find dy/dx: %3D a) у %3D сos u, и%3D—х/3 -x/3 u = b) y = tan u, и 3D…

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Q: (Note: This is a f(x) of Hyperbolic) e¯* + e* dx о ех — е х

A: We have to solve

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

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Q: d²y y = f(x) and x = e', prove that = xf'(x) +x²f"(x). %3D %3D dx2

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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 trapezoidal rule with…

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Q: - Evaluate the follwoing | r" exp(ax")dx where a + 0 and m+l = 1, 2, 3, ...

A: Given integral is, ∫xmeaxndx Substitute, u=am+1nxm+1dudx=m+1am+1nxm+1dx=1m+1am+1nxm+1du Then,…

Q: (a) Let I = dx. Show that I² = dx dy. R2

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

Q: Let z=e"In(xy), determine dx

A: Solving the problem by doing partial differentiation.

Q: E is the midpoint of FG DF = DG Given: Prove: DE I FG

A: From the data we have:

Q: +! dy dx x dx A- If Z = d'y x dx x dx? Prove that Z.Z = xp -1% NI X

A: A Given Z=d2ydx2+1xdydx. We need to evaluate Z.Z. Consider Z.Z.…

Q: Find e + Uy, Given that u(x,y) tan(x+11Xy+11y") .t/ - *א- w

A: Given ux,y=tanx+11x2y2+11y411-x2-y2

Q: b)S godx=? glx)dx=? ラg

A: To find the integrations

Q: Let z = = g(x, y) = e* cos y +y In(x – 1).

A: Let we havez=g(x,y)=excosy+yln(x-1)If x=s-t and y=s2-t2

Q: 53. Show that if u = x – y and v = y, then for any continuous f e* f(x – y, y) dy dx = e s(u+v) f(u,…

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Q: Assuming that f(x) dx = 3, F(x) dx = 5, and f(x) dx = 7, calculate f(x) dx. %3D (x) dx =

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Q: If x"y" = (x+y)** m+n m. X' d'y prove that = 0 dx?

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Q: dy 3) Determine the of : In (ху?) %3D х у dx

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Q: Let g(x) = kf(x) for all x E/= {x: asxsb}. Show that Jglx)dx = kJ f(x)dx if k<0.

A: To prove the above result we use the definition of lower and upper Riemann integrals. For the proof…

Q: (a) If f(x,y) = e" siny – e sinx then verify that fæy = fyx. %3D -

A: Given that  f(x,y)=e^xsiny-e^ysinx To verify the fxy=fyx

Q: i f(t) is given E ue of f(0.5) is

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Q: a²f If f(x,y) = e" sin (r + y), then prove that дхду дудх %3D

A: Hi! You have posted two non-related subparts. As nothing is specified, we are answering only the…

Q: Let C1 be the line segment from (1,0,1) to (0,3,6). Evaluate dx + dy + dz.

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Q: Given f(x, y, z) = xe"y + sin(xyz), find fyzz

A: Derivatives of: Sin x is Cos x Cos x is -Sin x u

Q: s continuous on la,b), then d f(x)dx = f(x) dx A) True B) False

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Q: given y = ƒ(u) and u = g(x), find dy/dx =dy/dx = ƒ'(g(x))g'(x). y = cos u, u = e-x

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Q: dy B] If y = e" In(u) and u = V1-x2, Find dx

A: To find

Q: Show that f(t) dt ) dx (x - a)f(x) dx.

A: To prove: ∫ab∫xbftdtdx=∫abx-afxdx

Q: Let f(x, y) = y cos (xy), then f.(x, y) = fy(x, y).

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Q: Given f(æ, y) = e"" Y' – z°y", show that fæy = fyæ.

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Q: @ Consider the DE, dx %3D dt x (2t -7) What meho can be uoed

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

Q: Show for Re(z) > 1 -dx = r(z) (2). et - 1

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Q: Let f (x, y) = csc(x + y³) ey , find дудх

A: The given function is  f(x,y)=csc(x+y3)exy. The main objective is to evaluate ∂2f∂y∂x.

Q: f and g are continuous on [a,b], then [* Grix)g(x)]dx = [(* F(x) dx)(√° xXx) dx) g(x) A True B)…

A: Given- If f and g are continuous on [a, b] then  ∫abf(x)g(x)dx=∫abf(x)dx∫abg(x)dx To determine…

Q: Let f(x,y) = x sin ry. Find: (a) fr(T,y) (b) fy(x, y)

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Q: " dy_ x +x*e prove that dx Q: If x =k (1+e II

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Q: If f(z) = sin(z 2) = U(x, y) + iV (x, y), determine U and V . Verify that the C-R conditions are met…

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Q: Evaluate fy and f, at the given point. f(x, y) = e³Y sin(x), (T, 0) fx(T, 0) fy(T, 0) %3D

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Q: Let f (x, y) = x+ y Evaluate . f (x,y)ds when x sin t, y = sin t

A: Explanation of the solution is given below...

Q: Prove that (x – 2)dx = – f,(x – 2)dx |

A: To prove that:∫13x-2dx=-∫31x-2dx

Q: dx dy. Evaluate by changing the order 4y

A: In the given question we have to evaluate the integration                ∫01∫4yyex2dxdy by the…

Q: dy If y = e" In(u) and u = V1-x2, Find dx

A: y = eu ln(u)       and   u = 1-x2 dydx = ?