At what interval is y=2r4- 4x2 concave upward? U x> 3 x< -- U 3 3 くxく 3 3 3 Jx> 3 3

Q: Frnd the exterma. O F(xy/z) = Xy z 2x +3y +りz=12. such that

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Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

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Q: 2x Ex FIND THE DERIVATI VES %3D

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Q: On what interval is the curve t2 X. dt y% = Jo t2 + t +2 concave downward?

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Q: Use the linear approximation to f (x, y) = √x/y at (9, 4) to estimate √9.1/3.9.

A: f(x,y)=xy at (9,4) to estimate 9.13.9

Q: of of and dy 6. For the function f(x.y) = sin ° (6x - 5y), find of df dy II

A: In partial derivative when take the derivative with respect to one variable consider other variables…

Q: Fundamental Theorem of Calculus.

A: ∫abfx dx

Q: Find fy and fy. f(x, y) = 13x In xy fx = 13 In y %D

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Q: Express in form y=f(x) by eleminating the parameter x = t + 3, y = 4t

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Q: dy when t = 7. dx Evaluate y = 2z? – 3z + 5 x = 4t +t t = z? +z+1

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Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)\/2.…

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Q: Use linear approximation to find y = L (x) of the function f (x) = = COS X about the point xXo = JT…

A: Use formula of  linear approximation

Q: QO use best linear approximation to (F(Xiy) = ²³ to estimate the value of f at the point (0.0),…

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Q: Find fr and fy- pry S(27, y) = /" 2e" dt %3D f.(r, y) = | f„(x, y) = | %3D

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Q: dy Find for y = dr dy dr || r J√3 + 0 3 + 4t2 dt.

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Q: 2. Show that the function u p(ry) + Vry v(y/x) provides the equation Pu = 0. ду? dx²

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Q: Solve dy / dx = 1 /( x^2 – 1) , for y(0) = 0. Find its maximal interval of existence %3D

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Q: Show that a fuinction F:R>R defired by 3 If I=y=0 1S continous ert (o0)

A: Continuity: Let a function f(x,y) be defined on an open disk B containing the point (x0, y0). A…

Q: 2. Show that the function u = p(xy) + VTÝ v(y/x) provides the equation „Pu dx² 0. dy²

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Q: Find f(x) if y = f(x) satisfies %3D dy 42ya3 %3D dæ and the y-intercept of the curve y = f(x) is 4.…

A: Given that, y = f(x) and   dydx=42yx13 and y-intercept of the curve y = f(x) is 4. we have to find…

Q: Ven dy' j + z k B - yi + 4x ĵ + 3²Ê %3D 3. i x (6x マ×(Gx - マ(マ.) - v* つさ

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Q: express in the form y = f (x) by eliminating the parameter x = t + 3, y = 4t

A: The given parameters are x=t+3, y=4t. The objective is to express in the form y=fx by eliminating…

Q: ,is concave up on interval x2-1 The graph of f(x)D OA (-1,1) OB. (0,1) В. Oc. (-1,0) U (1, 0) OD.…

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Q: . On what interval is the curve y = . dt +t+ 2 concave downward?

A: For y to be concave downward, it's second derivative y''  &lt; 0 We will use the Leibniz rule to…

Q: dy when t = 7. dx 13. Evaluate y = 2z? – 3z + 5 x = 4t' +t t = z? + z+1

A: Derivative of the function decides whether the function is increasing or decreasing. If the first…

Q: Evaluate dy/dx when t = 7 such that: y = 2z^2 - 3z + 5 x = 4t^3 + t t = z^2 + z + 1

A: Given                y=2z2-3z+5           (1)    x=4t3+t                   (2)    t=z2+z+1…

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

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Q: Fínd a differentiable curve y(x) that minimizes J = +

A: The objective is to find the differentiable curve yx that minimizes J=∫01y'x2+c2yx2dx if y0=0 and…

Q: Let f(x, y) = 2x² + 4y² + 2xy+ 10x + 3y + 9 Find D = frr · fyy - i

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Q: Evaluate S. (2xy – x²)dx + (x + y²) dy such that c is a curve bounded by y? – x , y – x² ?

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Q: dy when t=7. dx 13. Evaluate y = 2z' - 3z + 5 x = 4t' +t t= z' +z+1

A: Given eqn:  y=2z2-3z+5 where, dydx  at t=7 Now, dydz=4z-3x=4t3+tdtdx=112t2+1  ∴ t=z2+z+1 From the…

Q: Let f(z)=ex^2 = U(x,y)+iV(x,y) Verify Ux=Vy

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Q: If u- f(x) where y=J x+y%*34 show thal do

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Q: (a) Let f(r, y) = x - 3ry + 18y, where 3r?y- y- 6x = 0. Prove that f(r, y) has extrema at the points…

A: Calculate partial derivative of f(x,y) with respect to x and y ,

Q: Let ulx) be the solution of the IuP xy'-2y:x, yQ)=0 Evaluate y(32) %3D

A: In the question we have to find y(32).

Q: Show that the function u = p(xy) + VrY v(y/x) provides the uation x2 = 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: Find the interval on which the curve 1 dt 4+t+ 2t2 is concave upward.

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Q: 6lve the n dy equation + (acos Han x) dy +y cou2x = Castoc by changingthe Independent vaiable.

A: Given differential equation is d2ydx2+(2cosx+tanx)dydx+ycos2x=cos4x            (1) Comparing with…

Q: а. max f (x, y) %3D 4x + 3ху + у S. t. х+4y— 29 3D 0 х+ 4у — 29 — 0

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Q: Find the analytic function f(z) = u + iv if u = 2 cos x .cosh 2y cos 2x + cosh 2y

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Q: f(x, -0.0494 -0.3662 etter estimates by using Ar = 0.01 and Ay = 0.01. %3D 0.0516

A: Here we have to use difference quotients with ∆x=0.1 and ∆y=0.1 to estimate the fx(1,3) and fy(1,3)…

Q: Show that the function u = 9(ry) + /TY v(y/x) provides the uation ‚²u y? 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: xyz f(x.y.z) = et ot function is given P(2,,4) in point fux + fyy + fzz colculate.

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Q: On what interval is the curve t2 dt t2 +t+2 y = concave downward?

A: The given curve is: y=∫0xt2t2+t+2dt Using fundamental theorem of Calculus says: ddx∫axf(t)dt=f(x)…

Q: f(x, y) = /32² + 3y fz(4, 5) = VT23 %3D

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Q: Find the extrema of the function f (r, y) = y(x² + (In y)²), y > 0.

A: Second derivative test of two variable  function is Da,b=fxxa,b×fyya,b-fxya,b Then  If Da,b&lt;0,…

Q: Find all values of x and y such that fx = 0 and fy = 0 simultaneously. 13. f(x,y) = e*»+y?

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Q: Express in form y=f(x) by eleminating the parameter x = e−2t , y = 6e4t

A: Here, x=e-2t and y=6e4t

Q: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

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Q: Use the linear approximation to ƒ(x, y) 12x² at (3, 9) to estimate f(3.1, 8.8). y2+7 (Use decimal…

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