Let F(x) = e -5¢4 dt. Find the MacLaurin polynomial of degree 5 for F(x). Use this polynomial to estimate the value of r 0.12 ,-5x4 dx.

Q: In deriving the three point formulas, we use Lagrange polynomial. L'o(x) at x = xo is (notice the…

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Q: Find the average rate of change of the function over the given interval. f(t) = 13 + cos t a. - T, 2…

A: given f(t)=13+cos(t) To find the average rate of change of f(t)

Q: Find the gradient Vf of the function f given the differential. df = (342 + 1) ve" da + a° e® dy Vf =

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Q: Let y = f(x), where dy f(x) = = 3 Find the differential of the function. x³ + 3 3 X

A: Find the differential of function

Q: Let y = f(x), where f(x) = 5x² + 5. Find the differential of the function. dy = X

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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 differential df of the function f given the gradient. Vf = (5x + 6e" ) i + 6xe' j. df =

A: For the solution of the problem follow the next step.

Q: Apply the Fundamental Theorem of Calculus to get the following derivative. d In (t² + 1) dt dx 1

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Q: Use the total differential to find the slopes of the indiffa of the following utility functions: a)…

A: a) slopes of the indifference of the following utility functions  ux1,x2=x1x2 mux1=dux1,x2dx1=x2…

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A: Given, The tangent line to the graph of y=ln(2x) is perpendicular to x+4y=1 Here, y=ln(2x) To find…

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A: To determine the second degree Taylor quadratic approximation, we need to first find the first…

Q: Let y = f(x), where f(x) = 7x³ + 3x. Find the differential of the function. dy = X

A: The differential of y is the derivative of the function times the differential of x,

Q: Calculate the error of approximation with EA for the following functions Fix) = In 3x. when x = 4…

A: EA = 0.0030056

Q: Use the Product Rule to compute the derivative: d. Find dt (e + 1)(t + 9)) at t = 13

A: Topic :- Derivative

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A: Given :                      sin0.0012 To determine :                 The appropriate f(x) and a and…

Q: Consider the function F (x) = Sº,2 e* dt dF and determine the derivative dx O e^(x^4) No answer text…

A: Given that the function F(x), then we have to determine the derivative dF/dx .

Q: . Find all values of the constants m and b for which the function S sinx, y mx + b, x 2T is a.…

A: To find all values of m and b for which the function:   y=f(x)  =  sinx    x<π…

Q: of dx- = 0, then dy |=0. Prove that is a function f is harmonic

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Q: In deriving the three point formulas, we use Lagrange polynomial. L'o(x) at x = xo is (notice the…

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Q: 2x g(x) = |VI+t? dt 1+t2 dt %D

A: To find the derivative

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Q: t² – 4 - 4 f(x) = -dt 1+ cos²(t) 0.

A: Given:  f(x)=∫0xt2−41+cos2tdt

Q: Let y = f(x), where f(x) = (x-4)/(x^2+4).   Find the differential of the function.

A: Calculation: The first derivative of f(x) is given by

Q: Find the derivative (dy/dx) of the following functions: h) у%3D Зx7 —7х3 + 21x2 - i) y = (x² +…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

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Q: Find dy/dx implicitly and find the largest interval of the form -a <y <a or 0 < y <a such that y is…

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Q: Evaluate the second derivative of e22.1.png а f(x) acos(b/x) x2 if a = 345 and b = 0.6 at x = 5…

A: Given: Let us consider the given, fx=acosbxx2 where a=345 &amp; b=0.6 at x=5 using BDA with ∆x=0.06.…

Q: Vx +1 dx x + 2 (b)

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Q: Find the differential of the function. y = V6 - t8 dy %3D

A: Solution: The objective is to find the derivative of the given function

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Q: Consider the following function: y = f(x) = ln (2x² + 6x + 5) , for r > 0 (a) Calculate f'(0),…

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Q: Find the total differential. w = eбy cos(4x) + z7 dw (No Response)

A: Explanation of the answer is as follows

Q: Let f(t) = 4 sin(at) measure the height of waves in Horsetooth Reservoir with respect to time in…

A: The height function of the waves with time is ft=4sinπt

Q: In deriving the three point formulas, we use Lagrange polynomial. L'o(x) at x = xo is (notice the…

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Q: Ex2: Solve by using Laplace transform y'-x = et • x'+y = e=t, where, x = 0, y = 0,

A: The given system is, where initial condition is x=0, y=0. Now taking Laplace transform of equation…

Q: Consider the function Z = 2x²(1 – e-) where x and y are given to be 5 and In 5 respectively. Find…

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Q: Find the differential of the function. 7 + uvw Da + | Dov•([ Daw dT =

A: Given function is By using quotient rule of differentiation

Q: for the function f(x) = 2 cos(45x)o , determine:  the average rate of change for the interval 13  ≤…

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Q: Let f(x)= sec(x), find the linear approximation at x= pi/4 and use it to estimate sec(pi/5)

A: Given function: fx=secx At x=π4 fπ4=secπ4=2

Q: dx = +C (x+1)² X+1

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Q: Consider the function f(x) = e^x2−6x+5 . Find the value(s) of x at which the tangent line is…

A: Given thatf(x)=ex2−6x+5ddx(f(x))=ddx(ex2−6x+5)               =ex2ddx(x2) −6               =2xex2-6

Q: The third order derivative of the function y = In(1 – x) - at x = 0 is et O A. Undefined OB. C. 4 D.…

A: As per our guideline we supposed to answer only first question , kindly re post other as next…

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Q: Calculate the error of approximation with Ea for the following functions when x = 2, Ax = dx = 0.08

A: If the input of a function y=f(x) changes, its output also changes. The derivative of a function is…

Q: Si f(t) dt = x² – 2x + 1. Find f(x). 79. Suppose that

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Q: A. Find the derivative of the function at o P in the direction of A f(x, y) = x – E) V3sec-1(2xy)at…

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Q: Differentiate e w repect to X. expression (x2+y)" (use D fur dy)

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Q: Find the average rate of change of the function over the given interval. f(t) = 14 + sin t a. 0, T…

A: Given that

Q: Given y is the square root of x. Find dx/dt when y=2 and dy/dt= 1.75

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Q: Solve the linear ODE using an Integrating Factor. dy dx - 3y = 8e5x

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