1. Let ?g(x) =1/(x^2)+1 . 1.1 With h= 0.002, use the forward, backward and central difference formula to approximate g'(0.5) .

Q: 2) A function is given by 00 x* e=*dx. *e*dx. h(k) 00 Its values may be found in tables. Make the…

A: Recall that the Gamma function is an alternate form for defining the factorial notation. Gamma…

Q: 2 5. x=- 1+t2 2 y=, t(1+t?)

A: Given: x=21+t2, y=2t(1+t2).

Q: 8/7 Find g'(x) for g(x)=x g'(x) =

A: The given function is

Q: 1) Use forward and backward difference approximations with error of O(h²) and a centered difference…

A: Given function  fx = x2 e-3x7 Step size h =0.2

Q: Compute backward difference approximations for the first derivative of the function, y =[ e'nxP, at…

A: We have to compute backward difference approximations for the first derivative of the function,…

Q: Find the derivative of the function. (a) g(x) - log,(8x - 9x²) - (x),6 (b)

A:

Q: Given the table of values below, find h'(1) if h(x) = Xx 1 f(x) 1 g(x) (x) 2 f'(x) 3 g(x) -3 g'(x)…

A:

Q: Compute backward difference approximations for the first derivative of the function, y = e*cos(x?),…

A: We have to compute backward difference approximation for the first derivative of the function,…

Q: Compute central difference approximations for the first derivative of the function, y = e'cos(x?),…

A:

Q: Compute backward difference approximations for the first derivative of the function, y = log(x? +…

A: Given is the function y=log(x2+1)2   .  It is needed to compute backward difference approximation…

Q: A developing country's gross domestic product (GDP) from 2006 to 2015 is approximated by the…

A: Given: The GDP of a country is given using the function: Gt=-0.3t3+3.6t2+54 (a) Firstly find the…

Q: d steps for each problem

A: Here we have to find the derivative of  1) f(x)=e-x2 2) f(x)=ln(x3-5)2 3) f(x)=lnex

Q: Calculate G' (-4) to 3 significant figures where G(x) = (-4x – 2)'°(-2x² + 1x + 4)12

A:

Q: Suppose g and h are functions such that g (x) = ln (1 + h (sqrtx)). Find g'(4), given that h'(2) = 1…

A:

Q: A table of values for f, g, f', and g' is given. f(x) g(x) f '(x) g'(x) 1 3 2. 4 1 8 7 3 7 7 9 (a)…

A: Solve the function

Q: Use the graph of fand g. Let p(x) = f(x)g(x) and q(x) = -2 10 8 6 4 2 (a) Find p'(4). p'(4) = (b)…

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Q: 1. f(X)= xpi - pi(x) + pi/x + pix - cos (pi)

A: Given, fx=xπ-πx+πx+πx-cosπ We know that dxndx=nxn-1daxdx=axlnx

Q: Compute central difference approximations for the first derivative of the function, y =[ elnx)2 , at…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.