Given f(x,y,z) = 7xyz where x = sin(2t), y = cos(2t) and z = -1t. Find df/dt at t = -1. %3D Give your answer correct to two decimal places. Answer:

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A: Chain Rule Let us consider the function z=f(x,y) where, x=g(t) and y=h(t) Differentiate the function…

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Q: Given a = 40 sint + 12 and y = 40 cos t + 29 da (i) dt dy (ii) dt %3D dy (iii) dx ||

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Q: Solve the following DE's using Integrating Factor by Inspection or by applying Table 1. y(y² + 1)dx…

A: (1) The given differential equation is: y(y2+1)dx+x(y2-1)dy=0ydx-xdy+y3dx+xy2dy=0Divide both sides…

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Q: The displacement of a structure is defined by the following equation for a damped oscillation: y=9e…

A: The displacement of a structure is defined by the equation  y=9e-0.7tcos4t…

Q: x2 dy Find - for y = x dx -for y =x cos t?dt. sť dt. 2

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Q: Given x = 2 cos t + 8 and y= 4 sint dx (i) dt dy (ii) dt dy (iii) dx ||

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Q: (a) Find the differential dy. y = cos(x)

A: Differentiate the given function with respect to 'x' and find 'dy'.

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Q: b) Find fo dy for y = Vt-1 t = sec?x sint

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = (x+1)/(3x-5)   dy=

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Q: 1. y = √2x +7 2. y = √7+√√3x + 1 3. y Arctan√1-x²

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Q: a. S ya +1 b+y+cya+1 b. ft² cos 3t dt dy where a 0 and c = 1/(a + 1).

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Q: (a) Find the differential dy. y = tan(x) dy = sec?(x) (b) Evaluate dy for the given values of x and…

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Q: Q2: Suppose the electric potential at (x, y) is given by f(x, y) = 0.5 Ln(x² + y²) estimate the…

A: In this question, we have to find the error in f(x,y) and percent relative error for the given value…

Q: Given x = 2 cos t + 1 and y = 8 sin? t %3D dx dt dy dt ||

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Q: Find dw/ dt at the given value for the following functions 1) w=x² + y²₁ x = cos(t), y = sin(t), at…

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Q: The displacement of a structure is defined by the following equation for a damped oscillation: y=9e…

A: Displacement Of A Structure Is Defined By The Following Equation For A Damped Oscillation: y = 9e^…

Q: Find the total differential dw. 4. w = e*" – sin(yz) -

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Q: The radius r and height h of a right circular cylinder arerelated to the cylinder’s volume V by the…

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Q: Find the differential of the function. z = e-5x cos(9xt) dz = dx + dt

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Q: Given x = 70 sint + 13 and y = 70 cos t+ 22 dx (i) dt %3D dy (ii) dt dy (iii) -

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Q: a)  Find the differential dy. y = cos(?x) dy = ?       (b)  Evaluate dy for the given values of x…

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Q: (b) Calculate e cos(Tx) dx using integration by parts as many times as necessary.

A: Given: ∫excos(πx) dx The formula for integration by parts is given as…

Q: Given z = sin(1 - 2). x = 2 – ts and y = 2t – s - then calculate when t = -1 and s = -1. dt

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Q: Given y = 4e* + In x, find the differential dy. %3D

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Q: H.wl: Find L St. sin 2t.dt -3t {e p1 p2

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Q: Step 3 The total differential dz for the function z = x?y is dz = ydx + dy.

A: We need to find dz.

Q: r nosへSう'" ( メンン 2 COS(SIn (x))

A: Let, cos(sin-1x)=t⇒sin(sin-1x) 11-x2dx = dt⇒x11-x2dx = dt...(1)

Q: (dr Ifr=a cos ti +a sin tį+ at tan 0 k, find dt dr at t = 0. dr?

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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: Find the differential dy and (b) evaluate dy for the given values of x and dx. y=ex/10 , x = 0, dx…

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