B. Suppose that Z = f(x.y) is given implicitly by an equation F(x.y.z) = 0. Prove that dz/ax = -Fx/Fz and az/ay = -Fy/Fz %3D

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

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Q: Compute the following derivative. [P(i+5j-5tk) (e'i + 5 e'j-3e -k)] dt [P(i+5j-5tk) (e'i+ 5…

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Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

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Q: Suppose y = (x + 1)5, and both a and y are functions of t. If. dy :1, find dt dx when x = = 1. |3D…

A: Given data:   The given function is y=(x+1)5. The first value given is dy/dt=1. The given value of x…

Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

Q: If g(x) = ªſ*'[e'− In(2t+1)]dt, find g ''(x) . - dx -2 4 A + (2x + 1)2 Be-In(2x+1) 2 C (2x + 1)² 4 D…

A: Given that,      gx=ddx∫-2xet-ln2t+1dt

Q: Compute the following derivative. d (i + 2j - 2tk) • (e'i+2 e'j- 4 e -'k)] dt (i+2j- 2tk) • (e'i+2…

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Q: Given f(z) = | t2 – 16 dt 1+ cos²(t) OS At what value of a does the local max of f(x) occur?

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Q: c(x)=2x2-7x; c(0)=4,000

A: answer is in next step

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…

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Q: 1 use the formula L = dt to find the length of the curve dt dt 1 X = y = t° for 0st s1

A: according to the guideline, we are allowed to answer the only the first question  please repost…

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using…

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Q: Suppose z is a function of x and y, and csc Vr² + yz = z"esin. Solve for dz and

A: A multivariable function is a rule that connects two or more variables. The partial derivative of a…

Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

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Q: 2. Show that the function u = (xy) + JTY v(y/x) provides the equation y² : 0. dy?

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Q: Find the derivative of the given function at P. (3, 3, 3) in the direction of u = 3i + 4j f (x, y,…

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Q: Verify the final value theorem of f(t) =1+et[sint + cost]. O- 1 1

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Q: Suppose that we use the midpoint to approximate f(x) dx and that h = 1 and |f"(c)| < 3. If there is…

A: Error bound for the Midpoint rules: Let f(x) is a continuous function a,b, having a second…

Q: Obtain dy from the following function y=e'

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Q: Find the linear approximation of f(x) = In r at a = 1 and use it to estimate In(1.14). L(2) = %3D…

A: Please refer the attached image for complete solution.

Q: find the solution of following derivative by Runge-Kutta method f(x,y) = -2x3+ 12x2 - 20x + 8.5 let…

A: Consider an initial value problem dydx=f(x,y) with the initial condition yx0=y0. Then Runge-Kutta…

Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: Find the linear approximation to f(x) = 1 and then use that to approximate close to 1.003 1 1.003

A: Given: The function fx=1x To find: The linear approximation to fx=1x close to 11.003, then…

Q: dw if: dt Q1) Using the chain Rule to find w = xy + 3z, x = sint, y 2 cost, z=t (x2 +)

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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: 2. If f(x,y)= te Vy of=D0 then show) that 49 c) of af =0 dxay

A: Consider the given function. fx,y=1yex-y24y (i) First, we have to show that ∂2f∂x2-∂f∂y=0. First,…

Q: For the functions z = f(x, y), x = g(t) and y = h(t), if g(1) = 3, h(1) = 2, g'(1) = –1, h'(1) = 2,…

A: To find- For the functions z = fx, y, x = gt and y = ht, if g1 = 3, h1 = 2, g'1 = -1, h'1 = 2, fxP3,…

Q: The tangent line to the curve y=f(x) is horizontal at where X = Xo f f(xx) = 00 A O f(xo) = 00 .8 O…

A: The tangent line to the curve y=f(x) is horizontal at where x=x0 if

Q: Obtain dy from the following function y= e v*

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Q: 3) Evaluate numerically the derivative of f(x)= x.sin(x) - 1/x² at x = 0.7 with h = 0.01. Use the…

A: Given: The function, fx=xsinx-1x2.   To evaluate: The derivative of the given function at x=0.7 with…

Q: Suppose that n # 0 and n # 1. Show that the sub- stitution v = y!-" transforms the Bernoulli…

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Q: valuate |v(t)dt 1

A: We have given a graph in which the velocity v(t) of an object moving along a line is given where…

Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)

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Q: Assume y' means dy/dt. Solve y′′+ 4y′+ 4y= 0, and then using y(0) = 3 and y(1) = 5 find y(t), and…

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Q: If y = x(x – 1)* then y' at z = 2 is equal to

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Q: 10.Show that F(x, y) = (1 + xy)e*yi + (ev + x?e*y)j is conservative and find a function "f" such…

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Q: Assume y′ means dy/dt . Solve y′′+ 6y′−y= 0, and assume that the coefficients in your y(t) answer…

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Q: Evaluate dt dW at t=0 for the function W = e' – In x , x = t², y= In t

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Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

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Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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Q: a) If d'r = 3, when t = 0 we have dt? dx 0 and x=0, what is x as a function of dt t?

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Q: For given function f(x, y) = sin(y+ e*), match the derivatives fx, fy, fxy, f xx with the correct…

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Q: Consider the function y defined implicitly by 3(x2 + y2)? = 100xy. Use the linear approximation at…

A: Given : 3(x² + y²) = 100xy

Q: Solve the following problem dw dw + x dt 1, -00 0, %3D dx with w(x, 0) = f(x).

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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: Find the value(s) of @ for which y = cos ot satisfies d'y + 16y = 0. di? Enter your answers in…

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Q: Suppose X has pdt f(x) = - z(1 +x) which one is the pdf for Y 2X. (A) f)D- (8) f0)=- z(l + 4y) (4 +…

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Q: 6. Given the implicit curve, x2 - In (=) = 1, Write the linear approximation L(x) of the tangent…

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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: Consider the expression: ey = 4x + y* , In which y is an implicit function of x , after derivation…

A: Given problem :- ey =4x+y4 , find y'