1. If fo f(x)dx = 9 and f f(x)dx = 3, find 2f(x)da. 2. a) If g(x) is measured in pounds and e is measured in days, what are the units of g(x)dx? 2. b) Let G(x) = L (t? – sin t? )dt. Find G' (x). -

Q: Given the differential equation cos x = y sin x, then dy dx 24. y = In (sec x) + K B Iny =In(secx)+K…

A: Here we will solve the differential equation.  Here we will use the integration  formula of tanx.…

Q: Q:: If In /x2 + y? =sec(), use implicit differential to proof the following: - -x(²+y²). sec̟. tan?…

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Q: 18. y = x/I - x?

A: Differentiation:- The derivative of a function of real variable measures the sensitivity to change…

Q: 14. Solve the equation d?x 3 +2x sin dt2 dt dx given that at t = 0, x = 0 and 1. dt nent

A: See the details solution in below

Q: 5. If the function y = y(x) is such that dy + 2y = x cos r, dr use the integrating-factor method to…

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Q: 4 the second order For the function y = 4 e" - - d'y is derivative dx? 4e + 8x-3 O 4e" + 4x-2 -3 O…

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Q: find the differential dy. Hence, estimate the value of 1+ (1.023 2H y =

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Q: Let f (x²) be a differentiable function. Which of the following function is the integrating factor 1…

A: Concept:

Q: (1) хdy — ydx — Vx? + у? dx (2) — Зу? — у? sin x dx (3) (x2 + 1)4 — у2 + 1 dy dx

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Q: a) The velocity v and time t are related by the first order differential equation below. Find the…

A: (a) The given equation  dvdt-15v tant5=20...(1) comparing it with dvdt+P(t)v=Q(t) So,…

Q: 4 If y = In(8+ x4), find the differential dy. Your answer will be in terms of x and dx. Enter dæ as…

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Q: Q5) find the derivative 1. x = sin and y = sin+ cos if taken together, satisfy the differential…

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Q: 9. Sinte)e x(t² + 1)dt = x ,(t² + 1)dt S' 2* dx < S, xdx 10. dx = dx + dx 11.

A: 9.∫ln(e)0ln(e)ex(t2+1)dt=x∫0e(t2+1)dt10.∫012xdx≤∫01x dx11.∫131xdx=∫151xdx+∫531xdx

Q: To be able to solve the differential equation dx = sin(x - y), use the substitutions A z = x- y, dz…

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Q: 1. Find the differential of w = x cos y – y sin x.

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Q: (y sec² x + e' cos x – xe' sin x) dx + (xe' cos x + tan x) dy = 0

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Q: -cosh(x)dx 18) St?cos(2t)dt S 2y²e»*dy 19) Sxeax+1dx dx Sx²e2*dx 20) S x-x2 ) (2?/ª x)°e-In(x²)e3×dx…

A: We have to find the integration.

Q: 7. Find the differential dy for y = x2 – 4x + 6, then evaluate it when x = 2 and dx = 0.1 -

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Q: Find the differential dy of the given function. y = ln sqrt 5-x^2 dy=

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Q: Find the differential dy of the given function. (Use "dx" for dx.) 6. y = 2/x +

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Q: The term M(x, y) dx + N(x, y) dy becomes an exact differential if the left hand side above is…

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Q: Q:: If In /x2 + y? =sec(), use implicit differential to proof the following: - dy -x-(x2+y²). sec.…

A: Please see the explanation below..

Q: 87. Find the value of dy/dt at t = 0 if y = 3 sin 2x and x = t+pai

A: Given, y=3sin2x,  x=t+π y=3sin2t+2π we know, sinA+B=sinAcosB+cosAsinB sin2t+2π=sin2tcos2π+0=sin2t…

Q: Let y = e/3 Find the differential dy when x = 5 and dx 0.2 Find the differential dy when x 5 and dx…

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

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Q: T. Selue the ff. differential epnotion ) xy (xdy tydy) = ky'dy; when yol; x=2

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Q: 8. If y = xi, then the value of the differential dy as x changes from 16 to is (A) * (B) 5 (c) (D)…

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Q: 7.) (y sec² x + e cos x – xe³ sin x) dx + (xe³ cos x + tan x) dy = 0

A: Recall: In an equation of the form Mdx +Ndy=0 , first check the condition of exactness i.e, ∂M∂y…

Q: A point is moving along the graph of a given function such that dx/dt is 6 centimeters per second.…

A: Given Take derivative with respect to t, derivative of y is dy/dt  and derivative of x is dx/dt

Q: 19. State the order and degree of the differential d y d³y equation dx dy Cosx dx +2 + dx? а. 3, 2…

A: Order of the differential equation The highest derivative in the differential equation is the order…

Q: 2. The exact differential d xdy - ydx what is the d(xe")= x?

A: Let's find.

Q: 14. Solve the equation d2x dt? -3 + 2x = sin t dt dx given that at t = 0, x = 0 and = 1. dt gent

A: We have a differential equation d2xdt2-3dxdt+2x=sint The initial condition is that at t=0 we have…

Q: 1. The exact differential d(xy)= xdy+ ydx, what is the d( = 4x' y'dy+2xyʻdx. 2. The exact…

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Q: The velocity v and time t are related by the first order differential equation below. Find the…

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Q: dx dy Suppose x and y are functions of a third variable t. If sin²(x)+cos²(y) =- and dt 1, what is…

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Q: 6) g(z)= . cos(t) dt

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Q: Let y = tan(4r + 4). Find the differential dy when x = 1 and dæ 0.4 Find the differential dy when x…

A: Given that, y=tan4x+4 differentiating both sides with respect to x, we get…

Q: The concentration c of glucose in the blood with respect to time t is given by the dc differential…

A: Given: The concentration c of glucose in the blood with respect to time t is given by the…

Q: E valuate dt + seck tan x dX

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Q: Find the differential dy of the given function. (LUse "cx" for dx.) x +3 3x

A: We will solve the problem

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 7x + (sin(x))² dy = Need…

A: The solution is :

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 2√x + +√x dy = Need Help?…

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Q: 3 a) Find the exact integer value of a for which tsin (at)dt == ft sin (xt) dt = -². where a1. T

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Q: Find the differential dy of the given function. y = x(1 − cos x)

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Q: A 15 ft ladder leaning against a wall begins to slide. How fast is the top of the ladder sliding…

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Q: If y = In(6 + x8), find the differential dy. Your answer will be in terms of x and dx. Enter dx as…

A: topic - differentials

Q: Verify if the given function is a solution of the indicated differential equati 1. y = In sin( x +…

A: Since you have asked multiple questions in a single request. so we will answer only the first…

Q: 2. Find the following derivatives. (a) y = log; (xe*Y loz Leet (c) y = 38z2-5 (e) h(v) = e-2"…

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Q: Given the differential equation (ye-* - sin x) dx – (e ¬*+ 2y) dy =0, what is the value of f'(y)? (A…

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Q: Q: If In/x2 +y2 =sec(), use implicit differential to proof the following: - dy (²+y*). sec?. tan?…

A: lnx2+y2=secyx