Show that X. dt f(x) J3 V1 + t4 is one-to-one. f'(x) = Since f'(x) O for all x, f is increasing v on (-0, o). Thus f is one-to-one. Find (f-1)'(0). (f-1)'(0) =

Q: 1. Find the first partial derivative of z with respect to x if x'y+ y°z+ z'x = 11.

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Q: Find the derivative of In(3t³ – 2t + 1) and then calculate S; + 3 dt (use integration by…

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Q: 2) Compute the approximate derivatives of In x I+ x2 fCx) at x-2, using three- endpoint formula…

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Q: az Find if yz – In z = x + y ax

A: To find: The partial derivative ∂z∂x, if yz-ln z=x+y. Calculation: The partial derivative ∂z∂x can…

Q: Determine if the improper integral converges or diverges: 1 dx. 1+x²

A: Our Aim is to determine whether the improper integral given below converges or diverges∫0∞11+x2 -(i)

Q: 1 Prove that the integral : Tz dx is convergent. 1+x

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Q: Calculate the derivative d In (t)dt dx 5 using Part 2 of the Fundamental Theorem of Calculus.…

A: Given ddx∫x5e7xlntdt.

Q: If U = lx+my,v=mx-ly then prove that partial derivative of x

A: Given: u=lx+my v=mx-ly   To show: ux=-vy and uy=vx

Q: a?f (or and y. that is, f(x,y) = e² with respect to ayax axay Calculate the second-order partial…

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Q: Compute the second derivative of  f(x)=ex+x  at x = 2 using a step size h = 0.2  The backward…

A: According to the question; f(x)=ex+x                                                     ; x=2step…

Q: 2. Let f(x, y,2) = z-sin(xy), x = t, y = In t, z = e. Find derivative of f directly and by using…

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Q: Determine whether the improper integral diverges or converges. dx 1.f (2x-1)³

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Q: Determine whether the improper integral diverges or converges. dx 1.So (2x-1) 7 dx 2. x +1

A: We have to determine whether the improper integral ∫-17 dxx+1 diverges or converges.

Q: F(x)= ]7+1 3x t dt 2 F'(x) = %3D

A: We will find the derivative using Fundamental Theorem of Calculus.

Q: Solve for the partial derivative with respect to x, y and z f(x, y, z) = x²y + xy² + 2xyz

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Q: 2.Evaluate the total derivative of u with respect to x for u = 4x4+3y² + 3z² when y = sinx and z =…

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Q: Determine whether the improper integral converges or diverges

A: Given: ∫2∞ 1x-1 dx To determine: Given improper integral converges or diverges.

Q: · F(x) = 5* (S₁²¹6 (√₁+ u²) du) dt

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Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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Q: Let f(x, y,z) = z-sin(xy), x t, y Int, z et1. Find derivative of f directly and by using chain rule…

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Q: Compute the partial derivative fxxyz for f(x, y, z) = cos(cos(x3 + z2 )) + x2 ln(y2 + z2 ).

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Q: Find both first partial derivatives. z = sinh(7x + 16y) az ax az ду

A: From the given problem: z=sinh7x+16y As we know that: The chain rule: fgx'=f'gx·g'x The Power law:…

Q: Find the partial derivative of f(x,y) with respect to y at the point (3,2) f(x,y) = ln(x^2y-xy^2)

A: A partial derivative of a function of several variables is its derivative with respect to one of…

Q: Find the linearization of ƒ(x) = √(1 + x) + sin x - 0.5 at x = 0.

A: substitute 0 for x in f(x)=1+x+sin x-0.5 to obtain the value of f(x) at x=0 f(x)=1+x+sin…

Q: u = xz siny + yz cosx + xy tanz

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Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: (a) The centripetal acceleration of a particular wheel in a locomotive with respect to the angle…

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Q: The average rate of change of fx) = ax' Over the interval osxs1 IS a

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Q: From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)

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Q: Find the first partial derivative of w = In(1 + )at (2,0, – 1).

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Q: (b) 22). Compute the partial derivative frryz for f(x, y, z) = cos(cos(x³ + z²)) + x² In(y² +

A: Given f(x,y,z)=cos(cos(x3+z2))+x2ln(y2+z2).We need to find the partial derivative fxxyz for the…

Q: 2) Let f(x, y) = x sin(2y) + 5y¹. Find fyyyyyyyyyy (x, y) (10 partial derivatives), explaining how…

A: Here the given function is f(x,y)=xsin(2y)+5y4x. We have to find the 10 times partial derivative of…

Q: Find the slope of the tangent line to the graph of f(x) = x· 2e*cos-1t dt at x = 1 Jln x

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Q: Given function f(x, y) = 1+ xy - x - y. df a) using partial differential involving limits to obtain…

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Q: Compute the derivative of g(x) = cos(t²) dt. O 42 sin(z*) O cos(x*) -42 sin(z*) O 4a cos(a) O -…

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Q: Find both first partial derivatives. z = sinh(7x + 5y) az ax az ду || ||

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Q: If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O…

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Q: .2 x+15 dx Jx* +3 1

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Q: Show that the differential form in the integral is exact. Th (1,2,3) | 2xy dx + (x² -z°) dy -6yz dz…

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Q: Find both first partial derivatives. z = cosh xy2

A: Given: z=cosh xy2 To determine: ∂z∂x& ∂z∂y

Q: 55. Show that dx J+4 converges by comparing with x³ + xdx. -3 dx. х

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Q: Determine whether the improper integral diverges or converges. dx 1.fº. (2x-1)3

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Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: Find the derivative of g(x) = |. •r In z Vt2 +t+1 dt

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Q: Let f(x, y,z) = z-sin(xy), x = t, y = In t, z = e4. Find derivative of f directly and by using chain…

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Q: Letv = x2sin(v) + vexy, where X = s + 2t and y = st-

A: Solution is below.

Q: Does fn converges to L1 and L2 i.e the distance between fn and f goes to 0

A: By the theorem: A metric  on BE is the uniform metric du  . A sequence of bounded functions fn:E→ℝ…

Q: (b) Find the partial derivative, g where g(x,y)=sin' (2x+y). (c) Given z= In(2x+3y) with x 2s' (t-s)…

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Q: Solve for the partial derivative with respect to x, y and z f(x,y,z) = x²y + xy² + 2xyz

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Q: Suppose a particular investor derives utility function - U(x, y) - from owning x units of stocks and…

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