Let F(x) = | sin(7t) dt. 0, Find the MacLaurin polynomial of degree 7 for F(x). 0.71 Use this polynomial to estimate the value of sin (7x") dx.

Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 8x2 - 1 dy =

A: solve by implicit differentiation

Q: Let y = tan(5ax + 5). Find the differential dy when x 3 and dx 0.2 Find the differential dy when x =…

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Q: Let y = tan(5x + 4). Find the differential dy when x = 5 and dæ = 0.4 Find the differential dy when…

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Q: Find the MacLaurin polynomial of degree 7 for the function sin (ot) dt. F(X) = %3D

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Q: Find the linear approximation of f(x) = ln x at a = 1 and use it to estimate In(1.2). L(x) = In(1.2)…

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Q: 5.32. z = sin(x² + y?)

A: To find the differentials of third order.

Q: Use the modified Euler Method to solve the ODE = subject to y 1 when x 0 %3D dx 1+x on the interval…

A: To find y(0.3) by using the modified Euler's method.

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. ƒ(x) has a root in [0,1]. If we…

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Q: Let y=tan(2x+6) Find the differential dy when x=1 and dx=0.2 Find the differential dy when x=1 and…

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Q: Let y = tan(4x + 6). %3D Find the differential dy when x = 5 and dx: 0.4 %3D Find the differential…

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Q: Q4) A) Find by using chain rule if f = ( , u=-1, x=-1 dx ++1 B) Evaluate the following integral: V2…

A: Given f(u)=u-1u+12   , u=1x2-1    , x=-1

Q: Find of the following by implicit differentiation. Show solution. dx y sin x =x2 – 2y • sin x+ sin y…

A: This question is related to derivative.

Q: Find the general solution using Reduction of Order: y''+y'=cos 3x

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = - cos( 7x - 1 dy =

A: We have to find dy for the given function y=17cos7πx-12.

Q: The linear approximation at x 0 to f(x) = sin(6x) is:

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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: b) Find O Using the chain rule to find de x-1 dy of y= dy of y sin 1-xy ) Using the implicit…

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Q: Let y = tan(3r + 5). Find the differential dy when x = 3 and da = 0.1 Find the differential dy when…

A: Here we need to use chain rule of differentiation to find dy. According to chain rule,…

Q: Use the Beta and gamma function -1 n! 1- Prove that x™(ln x)"dx (m+1)n+1

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Q: If f(x) = x^2 sin(3x), find the differential dy

A: Consider the given: fx=x2sin3xy=x2sin3x Differentiate w.r.t. "x", dydx=ddxx2sin3xApply the Product…

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

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Q: Find dy dx' i) f(x) = Cos2x Sin²x %3D ii) f(x) = log,(x' +4)* e-* /2x - 5 -3x iii) f(x): (6-5x)'

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Q: Find the antiderivative F(x) of f(x)=12-pi(sin(x))+17cos(x), given F(0)=3pi

A: To find the anitderivative of the given function.

Q: Find and show the work for 2 (x+3)(3x+2) dx. (a) (b) SF (sin(2x) – cos x) dx.

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Q: Let y = tan(4x + 7). Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

A: Since you are asking multiple questions. We are answering only the first question as per our…

Q: dx J x2-4x+5

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

Q: Evaluate the Integral dx – (**V2Tan-1x-(Tan-1x)2 1-х4 '2Tan-1x-(Тап-1x)2 3. S х?/2Tап-1x- (Тап-1x)2…

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Q: Find the differential dy of the given function.    y = x tan x

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Q: y" +y' = cos 3x

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = -5x – (sin(x))² dy =

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Q: Find the value of the improper integral or state that it is divergent. (If it is divergent, enter…

A: We will calculate the definite integral using basic definite integral properties and if we get an…

Q: Let y = tan (2x + 6). Find the differential dy when x = 4 and dx = 0.2 Find the differential dy when…

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Q: The of the function y= e sin(3x)- In(5.x +2x+1) dx at (0,0) is: А. О В. -1 С. 1 D. 3

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: The approximation of the integral f(x-1) cos(x+2) dx using two points Gaussian quadrature formula…

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Q: Let y = tan(4r + 8). Find the differential dy when a = 4 and da = 0.3 Find the differential dy when…

A: Differential equation: - A differential equation is an equation that contains the derivative of an…

Q: Find a linear differential operator that annihilates the given function. (Use D for the different…

A: The annihilator of xn-1 is Dn The annihilator of xn-1sin βx is D2+β2n Now the given function is…

Q: Q2- Find for the following functions :- dx 1- y = (Inx)/tnx 2- y = x cos-1 x - v1-x² +sin-1x

A: We have to find dydx for the following functions... 1. y=lnx1lnx2. y=xcos-1x-1-x2+sin-1x

Q: . Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. f (x) has a root in [0]. If we…

A: Newton-Raphson iteration scheme is given by  xn+1=xn-f(xn)f'(xn) We use this formula to estimate…

Q: dt What is the linearization of h(x)= 6+ at x=1? cos (1 -1)

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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: (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: 3 Evaluate the definite integral dx. (x- 5)4 -2

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = arctan(x – 2) dy = ||

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Q: Let y = tan(3x + 8). Find the differential dy when x = 3 and dæ = 0.1 Find the differential dy when…

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Q: Find the actual error when the first derivative of f(x) = sin(2x) at *=1/8 s approximated by the…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 4x + (sin(x))² dy

A: The solution is given below

Q: Let y = tan(3x + 5). Find the differential dy when a = 4 and dæ = 0.1 Find the differential dy when…

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Q: 6 The coefficient of sin( 2r) in the antiderivative of F(x): F(x) = (cos( is

A: We have to find the coefficient of sin 2x.