2. Given f(x) = Vx and g(x) =5 -x. Find a). (fo g(x); b). (go f)(x) and give the domain for each nomnocition SLO 1

Q: If g(s,t) = f(s^2 - t^2, t^2 - s^2) and f is differentiable, show that t(∂g/∂s) + s(∂g/∂t) = 0

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Q: (b) f(x) = where A; E S™ – (det(Ao + x1A1 + ...+ xn An))/m, on {x | Ao + ¤1A1 ++xnAn > ► 0},

A:

Q: What is the maximum value of y = cos x. For -5 < x <? 1 2 O 1/2

A: Topic = Derivative

Q: The function yow) satisfies the differantial equation x dy + ay Cos(xx) ak y(1) = 1 , the valu of…

A: Given differential equation is  xdydx+2y=cos(πx)x,y(1)=1

Q: 2. If f (x) = Sn* et? 0, dt, find f'(x) V2t+sect

A: The solution is given as

Q: B: Expressand as functions of u and v both by using the Chain Rule and by expressing z directly in…

A:

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

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Q: hich z ∈ C the function e^(1/z) is holomorphic?

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Q: For the function f(x,y)= (x² + y²) tan(ln(xy)) + e(x-y) which of the following is the value of…

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Q: Given that f"(x) = cos(x), f'(T/2) = 2 and f(T/2) = 12 find: %3D - f'(x) = f(x) =

A: Given: f''(x)=cosx

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: Find the absolute maxlimum of frr.y)=xy subject to the Coustraint glxy)= x²ty²=/

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Q: 2. Find frxz for f(x, y,z)= z² e³xy

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Q: is stricly increasing on (0, T /2). sin x Prove that the function f(x)=

A: Given that: f(x)=xsinx

Q: \+etari), find f.. S, and f.- xyz 3. If f(x,y,z)= hn 2

A: We have to find fx , fy , fz.

Q: For f(x): cos(x) + 2, choose all values of c in the interval TT 37 guaranteed by Rolle's Theorem. 2'…

A: Given, fx=cosx+2 f'x=-sinx By Rolle's theorem, fx=cosx+2 is defined in the interval -π2,3π2, such…

Q: Find e + Uy, Given that u(x,y) tan(x+11Xy+11y") .t/ - *א- w

A: Given ux,y=tanx+11x2y2+11y411-x2-y2

Q: Having f (x) = 1 +e¬* sin(4x) and the interval [0,1] Apply composite Trapezoidal and Simpson's rules…

A: I have done by the direct method and trapezoidal rule and find the error by trapezoidal rule

Q: Find the following for z = f(x, y) = x? +5x2y3-y. az %3D ax

A: FOLLOW NEXT STEP

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

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Q: O Find all second order derivati ves for f(x,y) = Cos(2x) - x²e5Y + + 3y2

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Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

A:

Q: Let f(x)= sin(x) – e¯*, po=0, and p,=1, then by Secant method p2=

A: f(x) = sin(x) -e-x  p0 = 0 and p1= 1

Q: For the functions w = 8x + 3y, x= cos t, and y = sin t, express dw as a function of t, both by using…

A: The given function is w=8x2+3y2, x=cost and y=sint. We have to express dwdt as a function of t.…

Q: Given f(2) = , 1+ cos (t) = |. t2 – 16 dt 1+ cos²(t) f(x) : %3D At what value of x does the local…

A:

Q: 5. Given F(x) = cos (t) dt, determine F'(x). 2

A: Using leibniz rule  Explanation is given below....

Q: If f =x-e" and F=x'yi-2y'zj + xy'z'k, find: div(F x grad(yf )) at (4,1,-2)

A: The function                     Then, we have to find

Q: find the aradients of the functions below a)f(x, y) = e-3y cos4x

A: We have to find

Q: f [Mesin(2x) dx = e$in(2x) + C, then the M is equal to- If

A:

Q: Find the absolute extremum point(s) of f(x) = e1−cos x  on [−π/2, π), if any.

A: The given function is                                            f(x)=e1-cos x And we have to find…

Q: Let f(x) = – x^3 – cos(x), po= – 1, and p,= 0, then by Secant method p2=

A:

Q: Finf y' if x=Arccos(1-t), y=/2t-t2.

A: We can find the answer using chain rule as below.

Q: If u = f(x), then f- dx ++2x+1 +C for some constant k. Compute kf(1).

A: In this question we have to compute kf(1).

Q: lim, - „f(x) = 0, then fx)dx diverges Select one: O True False

A: The given statement is

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: w=x2+y2+z2,  x=cost,  y=sint,  z=et a).…

Q: Q3) For f(x,y) = Sin(x,y) find fryxy at (1,–). %3D

A: Given query is to perform indicated derivative operation.

Q: 19 Suppose that Ts Cx) centered at 2 for f (x) is gicn by Ts Ca):345Ca-2)+5 Cx-2)?ょ2x-2)+(x-2) Than,…

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Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: Given f(x, y) = y ln(5x 6y), find f-(x, y) = fy(x, y) =

A: The function is given by fx,y = yln5x-6y To evaluate : The expression of fxx,y and fyx,y.

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: If f(x, y, z) = In(x³ + yl² + 2®) + V (x12 + y6 + 23), then find fr, fy and f; at (1, 1, 1).

A:

Q: Given that f(x, y) - cos(x²) + 6e* sin y . Find fxyxyx · %3D

A: fx, y=x61+6y-cosx2+6exsiny Partially differentiating with respect to x, we get…

Q: Suppose that f(x, y) = e 42? - ly + 7z + 2y then find the discriminant of f.

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Q: 1. For the function (x, y) = x²y + 2xy² + sin(xy), compute fx , fy , fxx fyy , and fry

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Q: B. Suppose that Z = f(x.y) is given implicitly by an equation F(x.y.z) = 0. Prove that dz/ax =…

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Q: The function f : XI→ a + b cos x, is defined for 0 sxs 2n. Given that f(0) = 10 and that f (n) = 1 ,…

A: The range of a function is the values that can be obtained from the function by substituting all the…

Q: 2. Show that the function u - p(sy) + Vj (y/2) provides the equation 0.

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Q: of Find of and for the following function. ду 1(x,y) = (2x – 9y)5 %3D of 1 дх of 1 dy

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Q: Use the Quotient Rule to compute the following: t2 + 1 at t = -2 dt \ t2

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Q: 1 V1 – x z 1 – at x = 0 x, 2

A: Since you are asking part (c). We are answering only the (c) part for you.…