52. If F(x) = ƒ(t) dt, where f is the function whose granhis given, which of the following values is largest? (A) F(0) (D) F(3) reas. 67. Which J arct (C) F(2) (B) F(1) (E) F(4) 68. Whic Why )dx y A 69. Prov y3 f(t) 70. (a) %3D 0. 1 2 3 4 (b) 53. Each of the regions A, B, and C bounded by the graph of f and the x-axis has area 3. Find the value of Jse this fact 71. Le an

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

A: topic - derivative of a function

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A: The given details are as follows. y=tan-1sin tcos t -1 Observe the chain rule of differentiation as…

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A: Solve the following

Q: Suppose y = v2x + 1, where x and y are functions of t. dx = 9, find dt dy (а) If when x = 4. dt dy…

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Q: Can you explain the question step by step

A: Given: z = f (x,y) , x= e^s.cos(t) ,  y= e^s.sin(t)

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

A:

Q: Compute dy and ∆y for y = sqrt(x^3 + 1) for the change in x from x = 2 to x = 2.03. Is dy a good…

A: According to the given information, it is required to determine dy and Δ(y) for the given function…

Q: Can i get help step by step please

A: Given,

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A:

Q: 14. Determine dy/dx if y is a function of x defined implicitly by sin(x? + 2y)

A:

Q: `s): The area of the surface obtained by rotating the curve y = ln(3x - 2), for 3 ≤ x ≤ e², about…

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Q: Q1/ Evaluate So (x² + 3y²) dy dx using Simpson's 1/3 rule in x-axis and Simpson's 3/8 rule in y axis

A: 1 Given integral is ∫03∫01x2+3y2dydx. We have to evaluate the given integral  by using Simpson's 13…

Q: 4. Evaluate: S. yx²dx + xzydy + xz?dz, where C:x = sint, y = cost, z = t² , (0 <t< 1).

A:

Q: If y=x^4−5 and dx/dt=−1, find dy/dt at x=−3.

A:

Q: Suppose y = V2x + 1, where x and y are functions of t. (a) If dx/dt = 3, find dy/dt when x = 4. dy…

A:

Q: Suppose y = V 2x + 1, where x and y are functions of t. (a) If dx/dt = 15, find dy/dt when x = 4. dy…

A: Consider  y=2x+1 where x and y are function of t.

Q: suppose y = √(3x + 1), where x and y are both functions of t. If dx/dt = 2, find dy/dt when x=5

A:

Q: If x = 2t2 +t+1 and y=8t3+3t? + 2 then dy at t = 1 is dx

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Q: Let y(t) be the solution of dy/dt= 0.3y(2 − y) with y(0) = 1. Determine lim t→∞y(t) without solving…

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Q: If x =t-1+5 and y 6+t-2 then dy at t = dx is

A: topic - derivatives answer is 4

Q: Find the value of dy/ dt at t = 0 if y = 3 sin 2x and x = t2 +π.

A: Given : y=3sin2x, x=t2+π To find : dydt We can write dydt as, dydt=dydx×dxdt                    1…

Q: Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

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

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A: Given y=2x+1 dydx=dydtdxdt

Q: Suppose 4x2 + 16y2 = 100, where x and y are functions of t. dy (а) If dt 1 dx find when x = 3 and y…

A:

Q: 02/suppose 4x+ 9y 36 where x and functions of t Y are dy =1 Rind dX when x=2 and y = 215 3. if dx. 3…

A: differentiate with respect to t

Q: 9. Suppose y = V2x +1, where x and y are functions of t. (a) If dx/dt = 3, find dy/dt when x = (b)…

A:

Q: of Let f (x,y)=tanh-1(x-y) with x=e" and y= usinh (t). Then the value of evaluated at the point dt…

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Q: 4. Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t?, (0 <t< 1).

A: A line integral is the integral of a function along a curve. The function can be scalar-valued or…

Q: If y = x - 4x and x = V2r + 1, find dy/dt when t = 1= V2.

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Q: (b) If dy/dt = 2, find dx/dt when x = dx dt

A: By differentiating we solve the function

Q: Solve dy = ytan t, dt using separation of variables given the inital condition y(0) = 15. Assume the…

A:

Q: Suppose 4x? + 9y² = 36, where x and y are functions of t. If = 1/3, find dx/dt when x = 2 and dt y =…

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Q: For y= sintx/2 obtain dy/dx at x= 0.5 with Ax= 0.1 using: dy。+1-リ-1 (a) dx 24x dy Yj+1-Y;. (b) dx 4x…

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Q: II. Find dy/dx of the following functions: 4. ytan (tanh.x) 5. y=e³x sechx 6. y = √sech5x

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Q: Q1-If x= cot-1 VE, y = find dy d2y dx' dx² at t = 2. t+1

A:

Q: Suppose y = V 2x + 1, where x and y are functions of t. %3D (a) If dx/dt = 9, find dy/dt when x = 4.…

A:

Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx+ x?dy by the curve y = x and y = x2.

A:

Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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Q: Assume that x and y are both differentiable functions of t and are related to the equation: y =…

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Q: What is dy/dx at t = 1 when x = t^3 - t^2 and * Y = /3t – 1

A: Recall: If x=x(t) and y=y(t) then dydx=dydtdxdt d(ax+b)ndx =a.nax+bn-1

Q: If a = 5+ti and y = 3t - t then dy at t = 1 dz is :

A: as per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 1) Find dy for each OF Following functions du a) y = cosh (2n) + 4 ny cosh (1an 2) + 2y = e * %3D F)…

A: Product rule of differentiation:   Chain rule of differentiation:

Q: Q1-If x= cot- VE, y =, find 2 dy dy dx'dx at t = 2. t+1

A:

Q: if wa2ey-Inz find dw dt X=In (t*, 1) y=tant 2set

A: According to power rule of differentiation and according to product rule of differentiation . Also…

Q: Suppose y = (sq. root of) 2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt…

A: y=2x+1 Differentiating with respect to t, we get dydt=122x+1·d2x+1dt…

Q: Suppose y = V2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt when x = 4. dy…

A: we will diferenciate the equation of y with respect to t, and solve this.

Q: 19. Sobve (1-x*)-+m*y=0 dy=m dx where x=0, y=0,

A: