2 d²y 4): 1+ dx. dx² Find the: Туре: Order: Linearity: Why?: Unknown Function: Independent Variable:

Q: dy at (2, 1) when y? = x³ – 3x – 1 and dt da = 2 is 9. dt The value of %3D Select one: a. False b.…

A: The given equation is  y2 = x3 - 3x - 1.... (1) to find dy/dt at (2, 1) Given dx/dt = 2

Q: In what direction from the point (1,-1) is the instantaneous rate of change of f(x.y) = 8x* – 10x?y?…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. Rx, Y,…

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Q: Where f(x, y) y calculate (–1, 1) towards the point dv (-1, 3)

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Q: Q/ find the dy when y = (x+z)= リ=(メ+2)mx, %3D 2x Qul Fird dy すく e y= ノ

A: Answer

Q: dy If x = t - t3 and y = t2 - t, the value of at t = 2 is %3D %3D dx

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Q: dy If y = (t + 2t + 8) (6t² + 6), find %3D dt dy dt

A: The given question can be solved as shown in step2.

Q: dy dt t2

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Q: Find a gradient of the equation: F(x,y) = v2x + :- y sin a + 4 VF =?

A: Here, the given vector equation is: F(x,y)=2x+xy-y2sin x+4

Q: integrate ƒ over the given curve. ƒ(x, y) = x3>y, C: y = x2/2, 0 <=x<= 2.

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Q: Determine the order of the DE. a.) y' + y = 5y^2 b.) (dy)/(dt) = t c.) y' = y'' + 5t^2

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Q: Find the linear approximation to the equation f(, y) = 3. xy at the point (6, 4, 6), and use it to…

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Q: Fx to find Fy dy Assuming - 3x° + 6y + 3xy = 0 defines y as a differentiable function of x, use the…

A: The equation is  -3x2+6y2+3xy=0

Q: -dx. V1–16z² Consider For the u-substitution u = 1 – 16x², which is the new integrand in terms of u?

A: Given:-∫014x1-16x2dxTo find: new integration in terms of u by using the u-sbstitution, u=1-16x2

Q: Find the linearization of the function f(x, y) 155 – 2x2 – 5y² at the point (5, 4). L(x, y) = Use…

A: Given:      f(x,y) = √ (155 - 2x2 - 5y2 )     Point : ( 5 , 4 )  Now     Linear approximation f (…

Q: Find the linearization of the function f(x, y) = /36 – læ² – 2y² at the point (3, -1). L(x, y) = Use…

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Q: utt = 0; x € (-0o; c0), t E [0, o) equation for u(x,0) = at

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Q: Find the linearization of the function z = x/j at the point (3, 64). L(x,y)

A: According to the Bartleby guideline only one question can be solved at one time, post the remaining…

Q: Find the linearization of y=√x  at a=49. Then use your linearization to approximate √56. Show work

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

Q: dy/ dx-y/x= -y ^2 /x Is it linear ? does lt become linear with a substitution v = y^ 2? does lt…

A: given equation is  dydx-yx=-y2x

Q: J(2t-3)-e-t²,3t i. 2t – dt 3 2vlnx dx . ii. X 2 iii. (2y-3]12 kdy.

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Q: The temperature at a point (x, y, z) is given by T(x,y,z) = 200 e-x- 3y-9z) where T is measured in…

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Q: Find a gradient of the equation: F(x, y) = y + x³ – ay? + 3 %3D VF =?

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Gradient problem....

Q: Evnlunte: (а) (- xy) dydx (b) dr(x-) dy, where y, = Va? - x?

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Q: • Find the direction in which f(x,y) = yeY increases most rapidly at the point (0, 2). %3D

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: The given function is: f(x,y)=8yx

Q: af Calculate at point (-1,2) where f (x, y) = 8+ x² + 3y? dv and v = i+j. 10 2 5/2 V2

A: fx, y=8+x2+3y2  &  v=i+j Partially differentiating with respect to x, we get fxx, y=0+2x+0=2x…

Q: Since wCo) = -2 in the diferential equation 3 dw + 6 w =g OBtain wCt) and explain dt Be haviort t =3…

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Q: dy =r-ky, y(0) = y, dt

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Q: dy - f *P, = 7 dt y(0) = 4.

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Q: y = secx prove that d² y dx +y 2y

A: For y=sec x, we need to prove that d2ydx2+y=2y3. Here,            y''=secx''      =secxtanx'…

Q: dy If y = (t + 5t + 6) (2t² + 4), find dt dy %3D dt Submit Question

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Q: d?y e. dt? dy + 4y = 8t – 10, y(0) = 1, y'(0) = 75 %3D dt 2

A: As you asking multiple questions so I answered only first

Q: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

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Q: ds where t+s = 2s . dt Find %3D 6.

A: t+s=2s

Q: Find the linearization of the function f(x,y) = y + sin (x/y) at the point (pi,3)

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Q: ,use the linearity of L   determine L[f]. Q. f(t)=sinh bt, where b is constant.

A: Given, f(t)=sinh(bt), where b is constant To determine L[f].

Q: Determine the linearization of y = 4 – 2x at (1, 2). Then use it to approximate the value of y when…

A: It is given that, y=4-2x2  at 1,2 we have to determine the linearization of function. Then use it to…

Q: The temperature at the point (x, y) on a metal plate is modeled by T(x,y)=4e^−(x²+y)/2,x≥0,y≥0. (c)…

A: Given: The temperature at the point x,y on a metal plate is modeled by Tx,y=4e-x2+y2, x≥0, y≥0 To…

Q: Differentiate. R(t) = (t + e)(2 - VE) %3D R'(t) =

A: Given function is Differentiating both sides with respect to x by using product rule of…

Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

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Q: z=f(x, y) = 2x +3 y at the point (2, 2, 20) (ii) Use a linear approximation to estima

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Q: ds Find where Vt +s = 2s . %3D dt

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Q: Obtain the general solution using separation of variables dx = t(1 + t²)sec²x dt

A: Given: The differential equation dx=t1+t2sec2x dt . The given differential equation can be…