Consider the function f(t) = 3 sec (t) – 3t². Let F(t) be the antiderivative of f(t) with F(0) = 0. Then F(3) =

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Q: Find F'(x). SOLUTION IN HANDWRITTEN x 1. F(x) = sin √t dt 2. F(x) = sin t² dt

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Q: 2. dy sin x - y where f(n) = 0. %3D dx

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Q: let y=2 sqrt x Find the change in y, Δy when x=3 and Δx =0.3 Find the differential dy when x=3 and…

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Q: Find the differential of the function w=x^5sin⁡(y^5z^4) dw=  dx+  dy+  dz

A: Differential of a function is simply the derivative of a function. Also, d(uv) = u.dv + du.v

Q: x tan(yz) ey – 4x3z2 3: Find the total derivative of f(x, y, z) =

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Q: Find partial derivative of dx for the function f(x,y) given below exp 2x. siny .(at the point (In2,…

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Q: Let y = 4x2 + 4x + 3. Find the differential dy when x = 1 and dx 0.4 %3D Find the differential dy…

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Q: If flix.y)=XSin²(y)+y°Cos(x) prove that fn=2[Costy).Sin(y) ySin(x)]

A: First of all, we partially differentiate function f wrt. x and then we partially differentiate the…

Q: Find differential of the function y = (x² + 8)3. dy = dx. When x = 5 and dx = 0.05, compute the…

A: Solving

Q: Q4/ 1- Evaluate: f/2fy sinx dy dx ди 2- If u = x² + ey² ,x= sin 2t , y = cost² find at

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Q: Find dy/dx by implicit differentiation. 6) x3 + 3x2y + y3 = 8 dy A) dx x2 + 3xy B) dy dx x2 + 3xy x2…

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Q: Apply the application for integration dy/dx=2x+3 y(1)=2

A: Given: dydx=2x+3, y(1)=2

Q: 2ydx + x(2 + x²y) dy = 0 %3D

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Q: Let y=5x^2Find the change in y, Δy when x=3 and Δx=0.2Find the differential dy when x=3 and dx=0.2

A: To find the following parts. 1.)find the change in y (∆y), when x=3 and ∆x=0.2. 2.)find the…

Q: Find a set of solution. Integrating factors found by inspection.   y(x2 + xy2 - 1) dx + x (x2 + y2…

A: Given the differential equation y(x2 + xy2 - 1) dx + x (x2 + y2 +1) dy =0. We need to find the set…

Q: Given the function f(x,y) cos 2xーx3eY +āyン COS find te second partial olerivative fxy.

A: Let f(x,y) is the given function.Then  fx is the derivative of f with respect to x taking y as a…

Q: Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: dz Use the chain rule to find Ət z = tan (x – 8y), x = s cost, y = e² •Int Se dz 1+(x²– $y}² dt dz -…

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Q: Let y = 3x² + 3x + 4. ind the differential dy when x = 4 and dx = 0.4 ind the differential dy when x…

A: Given query is to find differential at given point.

Q: Q6. Using Rule l-IV to find an integrating factors. (x² + y² + x)dx + xydy = 0.

A: Given- x2+y2+xdx+xydy=0 To Find- The integrating factor of the above differential equation.

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

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Q: Find the total differential w = x2yz2 + sin yz

A: Partially differentiate w = x2yz2 + sin yz with respect to x and keep y and z as constants.…

Q: dx (2tx +x+ cos t) + (-sin x +t² +t)- = 0. dt %3D

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Q: Find the change in y, Ay when x = 3 and Ax = 0.3 Find the differential dy when x = 3 and dx 0.3 %3D

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Q: 1, use 2x2 + 3x + 2. If Ax linear approximation to estimate Ay Let y 0.4 at x = Ay 2

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Q: Let 2x2+ 3x+Y a) Find the differential dy when x = 1 and dx=0.1 %3D b) Find the difiea ial dy when…

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Q: Explain why the linear approximation to ƒ(x) = cos x at x = 0 is L(x) = 1.

A: The linear approximation, or tangent line approximation, of f at x=a is defined as Lx=fa+f'ax-a This…

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Q: The linearization of ex at x = 0 Derive the linear approximation ex = 1 + x at x = 0.

A: Given, ex ,x=0 We know that, The formula for the linearization is, Lx=fa+x-af'a

Q: .A telegraph cable is made of an outer winding around an inner core. If x is defined as the core…

A: Using double derivative test to get max value of x

Q: 8. Find a continuous solution satisfying dy dr + 2xy = f(x) where = x if 0 < x < 1 0 if x ≥ 1 off…

A: Solve the following

Q: Use the method discussed under "Integrating Factor found by Inspection". (x² + y² + 1)dx + x(x –…

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Q: (tiy t 3y" -x)dn + x (x+ Jdy = 0 2

A: Given differential equation is  4xy+3y2-xdx+xx+2ydy=0 find the general solution of the given DE

Q: The time rate of change of liquid circulating in two tanks is govemed by dy -0.02x + 0.02y, = 0.02x…

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Q: Find the total differential dw. 5. w = x tan¬ y – 2ªyz

A: The objective is to find total derivative dw.

Q: Determine the most general antiderivative:  f(x) = sec x tan x-2e^x

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Q: tion to (1+ x²) dy + 2xy = 4 that satisfies the initial condition y(0) = 0. dx %3D %3D

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Q: Let y=3sqrt(x) Find the change in y, Δy when x=2 and Δx=0.3 Find the differential dy when x=2 and…

A: We are going to solve

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 5x2 − 2 dy =  y = 5x −…

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Q: Find the differential dy of the given function. sec² x y x² + 2 sec 2x (2x²tan x + 4 tan x-2x)…

A: This question is based on quotient rule

Q: Find the differential dy. x + 2 y = 9x - 1 dy =

A: In this question we have to find we have differentiation of y.

Q: dy for y = dx 9t -dt. 9t + 1 iz's rule to find

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Q: Let y = 3x² + 8x + 3. Find the differential dy when x = 1 and dx = 0.2 Find the differential dy when…

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Q: Find the integrating factor μ(x) of y' + 4y - tan(x) = 0 such that μ(0) = 1. μ(x) =

A: See the details solution in below

Q: Suppose F(x, y) = 0 and y is a differentiable function of x. Explain how to find dy/dx.

A: It is given that F(x, y) = 0 and y is a differentiable function of x . For the function F(x, y) = 0…

Q: Let y=3sqrt(x)Find the change in y, Δy when x=5 and Δx=0.2 Find the differential dy when x=5 and…

A: Given function is Change in y is calculated as follows. when x=5 and Δx=0.2

Q: dy Find by using partial differentiation where y is defined dx implicitly as y=f(x) for the…

A: We use the chain rule and product rule to find the derivative.…