1+x (a) Find the approximation of f, dx using Simpson's rule with step size h 1+x2 0.25.

Q: Find the Differential of a Composite Function Original function                        y = f(x) =…

A: Applying chain rule we get:

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

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Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: find dy/dx of each equation using implicit differentiation. a. y4 -2y2x2 + 3x2 = 0 b. (x + y)3 =…

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Q: Find the general solution to the ODE using the method of Variation of Parameters: y" + y= cos² x

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Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) At the point (, (2n…

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Q: 1. Find the derivative. g(x)=(4x-2)^5-√(x^2+8)

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: 18 dx Integrate using trig. Substitution: S- x² V9– x²

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Q: 5. Consider the function f(r, y) = sin(x² + y²). (a) direction of (4,3). Find the derivative of f(r,…

A: The directional derivative is the rate at which the function changes at a point in the direction .…

Q: (a) Show that the derivative solution of this function y = x** is dy = x(**+x=1) [1+ x ln x (In x +…

A: The given function y=xxx Note:    Multiple questions are given, we are answered with only one…

Q: Find the linearization of the function F(x)=tan-1(2x)= arctan(2x) at x=0. Then use linearization to…

A: We know the linearization of the function f(x) at x=a    L(x) = f(a) + f'(x)*(x-a)   In the…

Q: Find the slope of the curve 2xy = In(e*) sin(x) at the point (2,2)

A: to find the slope differentiate  the equation with respect to x .

Q: Find the linear approximation of f(x)=ln(x) x=1 and use it to estimate ln(1.1). L(x)= ln(1.1)=

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Q: یک 2. G(x) = L tanz et et +3 -dt

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Q: V sin2(x32 - 1) dx, with u x32 - 1

A: Consider the integral ∫(√x)sin2 (x3/2 - 1) dx.

Q: dw of w -+ dt X y H.W: Use the chain rule to find the derivative dw with x= cos 1, y = sin? t, z =-…

A: We differentiate the function with respect to t.

Q: respect to x of/ /(3Vi-1) dt is 3x – 1 by the 2nd fundamental theorem of C The derivative with (A)…

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Q: 8. Find the length of the curve y = e on the interval 0, ln 2| %3D

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Q: Find the linearization of the function f(x) = sin(x) at a = π and use it to approximate the number…

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Q: 5) y>10 (3v-1) (1+5w)

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Q: cx+ln x Determine the equation of the tangent line to the graph of f(x) cosh (V2t – 1) dt at x = 1.

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Q: 2. Find y' by implicit differentiation. (5) xy =1+ xy

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Q: R(x) = F/2 π dx

A: We have to evaluate the integral: R→x=∫0π/2sin2x3x+1, lnx2-1,xx2+1dx   .....(1)

Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: (a) Find the derivative. = In(x) – In(x - 8) dy dx (b) Find the derivative. y = In X - 8 dy dx %3D

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Q: Q-1: find the derivative of y with respect to the given indepe 1. y = In(Inx) 2. y = In(In(Inx)) x…

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Q: 2. Find using implicit differentiation. Enclose final answers. dx (a) 4x³y² + x¹y³ = x + y = 0 (b) x…

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Q: 3/20 What is the equation of the tangent line to the function y = e*- arcsin) at x= 0 ? A) y- -(1+)=…

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Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

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Q: Find the linear approximation of f(x) = sin x, for x close to 0

A: The given function is: f(x)=sin x To find the linear approximation of it close to 0.

Q: The finite difference approximation of the first derivative in the simple implicit method used to…

A: given  ∂2u∂x2=∂u∂t to find the finite difference approximation of the first derivative in the…

Q: 6. Let y + xy - y = 8x*. a) Find dy/dx using implicit differentiation. b) Find the equation of the…

A: In implicit differentiation, when we differentiate y, we use dy/dx

Q: What is the process for finding dy/dx when y is an implicit function of x? Illustrate with an…

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Q: 2. About what point is the local linear approximation l(x) 1 of the function f(x) = tan- x 4 valid?

A: Let's Solve,

Q: Find the derivative of the function at Po in the direction of A. g(x, y) = x- (y/x) + V3 sec (2xy),…

A: we have to find directional derivative.

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz,at the point in the direction of A =…

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Q: cx+ln x Determine the equation of the tangent line to the graph of f(x) = [" = cosh (√2t - 1) dt at…

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Q: – (x²- 1) dx using P (1 -;*)-^;* / * m in terms of A?

A: Use simple integration formula.

Q: dw of w: dt x y Use the chain rule to find the derivative 1 with x cos t, y = sin t, z =- dw and…

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Q: Q2) Find the derivative of the function at Po in the directi g(x, y) = x – (y²/x) + V3 sec-' (2xy),…

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Q: 3.9.27 Find the derivative of y with respect to x. y = sec 1(5x2 + 1). -1(5x2 +1), x > 0 dy %3D dx…

A: Please see the answer in Step 2

Q: (a) Find thẻ đéřivătivė. rivative. 1 y = In(x2 – 6) 3 dy dx (b) Find the derivative. 3 = INVX2 – 6…

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Q: 2) Find second derivative d'F/dt? of 312-2 F? = 13 and find it at (t,F) = (-1,2)

A: We have to find the required second derivative at the given point.

Q: What is derivative d(y)/d(x) of "xsin(1/y^e)=(1-xy²)^½

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Q: 1. S(esin *cos x – acos 2x sin 2x)dx 2. S(etan x sec x- esecx tanx)sec x dx 3. S dx xvax - 16 3x-2…

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Q: 2. Find the linear approximation to y = sinh (3x) at x=2. State your answer in both exact form and…

A: Find the linear approximation of f(x) at a point x=2

Q: dw of w==+ dt x. y Use the chain rule to find the derivative with x = cos 1, y = sin ?t, z = - dw…

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Q: Find the differential of the function   y = θ3 sin(6θ)

A: Solution :-

Q: (D³ + 3D2 + 3D + 2)y = 0

A: Find out the solution.