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## Related Calculus Q&A

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Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

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

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Q: what is the maximum value of y=sinx, 0 less than or equal to x less than or equal to 2pie, and…

A: Given function y = sinx on 0≤x≤2π

Q: On the graph of f(x)=sinx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?

A: The given function is fx=sinx Differentiating w.r.t. x to both sides- f'x=cosx To find the critical…

Q: If (x, y) moves from (x0, y0) to a point (x0 + dx, y0 + dy) nearby, how can you estimate the…

A: The resulting change in function f (x, y) is given as:

Q: Show that y = -cosx In(secx + tanx) is a solution of y" +y = tanx

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Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORN 3x-4 1. y = Arctan 2. y = 2 Arccos (1…

A: y=Arctan3x-44

Q: 12. Show that F(x) = sinx – x cos x+2 is an antiderivative of f(x) = x sinx.

A: Given, F(x)=sinx-xcosx+2 To show that the above function is an antiderivative of f(x)=xsins.

Q: Find the linearization of ƒ(x) = √(x + 1) + sin x at x = 0. How is it related to the individual…

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Q: Find antiderivative of f(x) = cosx

A: We have to find antiderivative (Integral) of f(x) = cosx i.e ∫ cosx dx

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Q: find the most general antiderivative of f(x)= 2x^3 - sinx + 4e^x

A: We find the integral of f(x)= 2x^3 - sinx + 4e^x We separate the integral first.

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Q: The derivative of y=eev* +cosh x equals Select one: O y' =eev +sinh 2/x 「Oy=SeV全 + sinhx 2/x ev…

A: Given: y=eex+coshx To calculate: Derivative of y

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Q: (b) Find the partial derivative, g where g(x,y)=sin' (2x+y). (c) Given z= In(2x+3y) with x 2s' (t-s)…

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Q: From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)

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Q: Find the CRITICAL VALUES of f(x)=sin² x+cosx on the interval (0,2n)

A: Critical points are the points where the derivative of the function is zero or undefined. Our…

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Q: Let u = x3 + 1. Indicate how the limits of integration should be adjusted in order to perform the…

A: Given

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Q: If f(x, y) = y cos(x) – a° In(y), find the second partial derivative ду дх .A 3x2 = -2y sin(x) ду дх…

A: Option (a) is correct.

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Q: Show that f(x) = sin x (1 + cos x) is maximum when x = Hence find its maximum value.

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Q: Find the antiderivative of the function f(x)=3x-cos x-ln x

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Q: Plot f (x) = ln x − 5 sin x on [0.1, 2] and approximate both the critical points and the extreme…

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Q: 7. By differentiation (and having a suitable choice of integrating constants) show that L. f(s) ds+…

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Q: If f(x, y) = y² cos(x) – x³ In(y), find the second partial derivative ду дх

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Q: Find the first-order partial derivative with respect to x of f(x,y) = e5x siny.

A: To find the first-order partial derivative with respect to x, given function, fx,y=e5x sin y

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Q: The maximum value of y = sin x, 0 <= x <= 2p, isand occurs at x =__________ .

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Q: If Q = f (x, y) and considering increases in both variables, how is expressed the total differential…

A: Concept - By using chain rule of derivative

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Q: Find the antiderivative of the function f(x)=5x-sin x

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Q: If f(x, y) = ln(x + y), then total derivative or total differential of f at x = 3 and y = 20 is : Y

A: Given data: The given expression for the function is f(x,y)=ln(x+y). The given value of x is x=3.…

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Q: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…

A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of the…

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Q: The Derivative az/əx of sin(xy+z)-sin(zx- * :y)+sin(yz+x)=1 is -ycos(xy+z)-zcos(zx-y)-cos(yz+x)…

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Q: Usually in a method of solution for Homogeneous DE, after the substitution of y = vx (or x = vy) and…

A: In the method of solution for homogeneous differential equation, The equation is of the form,…

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Q: 23, zax + sec(x)cos(y) 0, y(0) = 0

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Q: Find the antiderivative for the given function. 3x tanh(x*) 1) In(cosh(x*)) +C 2) In(cosh(x*)) + C…

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Q: Find partial derivative af for the function f(x,y) given below exp 2x. siny .(at the point (In2, 0

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Q: first derivative y= 4in Gty) is dy 4.

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Q: Given function f(x, y) = 1+ xy - x - y. df a) using partial differential involving limits to obtain…

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Q: Find the family of antiderivatives of f(x) = sin 3x.

A: Given that f(x)=sin3x ...(1)

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Q: The maximum value of y = cos x for - < x< is 1

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Q: Determine the anti-derivative of Y = 2e3x +5 and use the fact that y(0) = 7 to %3D dx determine c,…

A: We first separate the variables and then integrate c= integrating constant Formula used:

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Q: If f(x, y) = y° cos(x) – x³ In(y), find the second partial derivative ду дх .A ² f ду дх 3x2 -2y…

A: Calculate partial derivatives

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Q: The derivative of y= sech-1(x sechx)+e$inh (Inx) equals Select one: – x sechx tanhx+ sechx O y:…

A: Given

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Q: Explain of the method of proving the derivative (dy/dx) of y=U(x)ᵛ⁽ˣ⁾ where U(x) and V(x) are…

A: y=uxvx, where ux & vx are the differential functions of x. To differentiate these type of…

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Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)"(») where U(x)and V(x) are…

A: The function is, y=U(x)V(x)

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Q: Determine the maximum/minimum point(s) for y=sin 2x– cos x – 4x on the interval 0 <x< 2n . The…

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Q: If f(x, y) = y² cos(x) – a° In(y), find the second partial derivative

A: Partial derivative problem

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Q: find x which minimizes the following function and its minimum with differentiation technique.…

A: We will find out the required solution.

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Q: find y' by implicit differentiation. ex/y=3x-2y

A: To find the derivative of the equation using implicit differentiation.

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Q: Find the length of y = ln (sec x) between x = 0 to x = π/4.

A: you meant to find the arc length of y=ln(secx). the formula for the length of the arc in the given…

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Q: 4. Find the first order derivative with respe. to x of the function u = In/x2 + y2 + z2 %3!

A: The function is u=lnx2+y2+z2

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Q: Find the critical point(s) of the function f (x, y) = xy + ln x + 2y . Then use the second…

A: Find critical points, nature of critical points and relative extrema of the given function.

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Q: Find the derivatives of the f: 1. y: sin (x²+3) 6. y= e tan 3x 7. y: e 2. y= tan (4x*) cot (3x-8) 3.…

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