Consider the function f(x) = x³ + 2x + 5. 1. Estimate the root to two significant digits using bisection method in the interval [-1.4, -1]. n Xn bn error an -1.4 0 -1
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A: Let us write the mathematical expression to a MATLAB expression in the next step.
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Q: 4.1. Derive the heat equation with a metal rod with variable cross-sectional area A(x). Using the…
A: We have to drive the heat equation with a metal rod with variable cross-sectional area.
Q: e following equations by conv ar complete solutions.
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A: Solution :
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A: According to guidelines I solve first 3 subparts so kindly request you to repost the remaining…
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Q: using Polar tics II, e the card Find the Q3) By using the polar find region enclosed by y = x² and y…
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Q: Taylor series of the following ) = ln(1+x), a = 0. ) = x² + 2, a = −1.
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Q: 3. Find the Maclaurin series of the function F(x) = foedt. Use it to estimate F(1/2) with an error…
A: We will use Maclaurin series of ex ex=1+x1!+x22!+x33!+......∞
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Q: Exercise (1-3): By Charpit method solve the following PDE Question Answer (1) p²x+q²y=z z =…
A: We have to solve the given problem.
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- Use the Remainder Estimation Theorem to find an interval containing x = 0 throughout which f(x) = cosx can be approximated by p(x) = 1−(x²/2!) to three decimal-place accuracy.Find the linear approximation of f(x) = (5 + x)n at x = 0. Use the approximation to estimate the value 5.024Find a root of a equation f(x) = 2x³ - 2x - 5 Using secant bisection method when the initial interval is (a= 1, b= 2) at a required tolerance of f(x)←(-0.003).
- calculate y(0,1) with the interval Δx = 0.025 using the Runge Kutta order 3 and Runge-kutta order 4 methodsFind an approximate solution of the first root of the following function using the secant method. Consider the interval [0,1-0,5] with an allowable error of 10^-2Find the root using the method indicated. [f(x) <0.0001 f(x) = x² + 2x²+x-1, (0, 1) f(x)=x3+2x2+x-1, (0, 1)using Secant Method
- Use the linear approximation (1 + x)k = 1 + kx to find anapproximation for the function ƒ(x) for values of x near zero. ƒ(x) = (1 - x)6Use the error term of a Taylor polynomial to estimate the error involved in using sinx=x to approximate sin 1Sketch the graph of the functions y=3x^2 and y= e^x to find an approximation x0 for the x-coordinate of their point of intersection. Use the Bisection Method to obtain an estimate of the x-coordinate of the point of intersection. Use as many iterations as necessary to obtain an estimate which is accurate to five decimal places.
- Use the linear approximation (1 + x)k = 1 + kx to find anapproximation for the function ƒ(x) for values of x near zero. ƒ(x) = 2/1 - xHow do I estimate the error R(x) when x < 1/2? Let f(x) = cos(4x), and it is replaced by P(x)=1-(16x 2 /2) an order 2 Taylor polynomial, centered at 0.Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1 Construct a Langrange Interpolating polynomial of degree 3 approximating f overthe interval [0.2, 0.8]. Find the actual error at x = 0.5?.thanks.