Estimate the sin 5(degree) using local linear approximation. State the differential and estimate the error in the approximation.
Estimate the sin 5(degree) using local linear approximation. State the differential and estimate the error in...
I need the error in percentage
(6 points) Estimate Af using the Linear Approximation and use a calculator to compute both the error and the percentage error. f(x) = V3 + x. a=1. Ax = 1 Af = 25 With these calculations, we have determined that the square root of 5 is approximately 2.25 The error in Linear Approximation is: .01393 The error in percentage terms is:
Let y = sin(4x). If Ax = 0.3 at x = 0, use linear approximation to estimate Ay Ay = = Preview Find the percentage error rounded to 1 decimal place. error = Preview
3. (8 points) Find an appropriate local linear approximation for the function cos(x) and estimate the value of cos 31°.
5) a) Use the alternating estimation theorem to give the maximum error for approximating sin 3 using a third degree Maclaurin polynomial for sin a. b) Use Taylor's inequality to estimate the accuracy of a fourth degree Taylor polynomial for sin a centered atfor 0 s a s
5) a) Use the alternating estimation theorem to give the maximum error for approximating sin 3 using a third degree Maclaurin polynomial for sin a. b) Use Taylor's inequality to estimate the...
1. Linear Approximation First, read Section 4.1 and the lecture notes of days 16 and 17. The steps for linear approximation of are as follows 1. Choose an objective function f whose value at r we want to estimate and choose a center value a closed to r 2. Compute the linearization L(x) - f(a)f'(a) (z - a) of the objective function 3. Compute L(x) to get the required approximation 4. Compute the second derivative and decide whether the linear...
a. Write the equation of the line that represents the linear approximation to the following function at the given point a. b. Use the linear approximation to estimate the given quantity. c. Compute the percent error in the approximation, 100•approximation−exact/exact, where the exact value is given by a calculator. f(x)=4e^x at a+0, f(0.02) a.L(x)=? b. Using linear approx, f(0.02)=? c. The % error in the approximation is=?
4. Consider the function f(x) = sin(x), x > 0. (a) Estimate f(r) - f(A), where TA is an approximation to rr. (b) Estimate Rel(f(A)) in terms of the error Rel (TA). - f(TA
4. Consider the function f(x) = sin(x), x > 0. (a) Estimate f(r) - f(A), where TA is an approximation to rr. (b) Estimate Rel(f(A)) in terms of the error Rel (TA). - f(TA
a. Write the equation of the line that represents the linear approximation to the following function at the given point a. b. Use the linear approximation to estimate the given quantity. approximation - exact| c. Compute the percent error in the approximation, 100. where the exact value is given by a calculator. exact f(x) = 2 eat a = 0; f(0.03) a. L(x)= b. Using the linear approximation, f(0.03) (Type an integer or a decimal.) c. The percent error in...
(a) Estimate the value of tan(0.85) using a linear approximation. Let your point be a = use the fact that tan(x) = sec'(x)=- . Give the calculator value to 5 decimal dx cos? (x) places for comparison. (b) i. Give a reason that the function f(x x + x +5 has at least one zero. ii. Use the derivative to show that it cannot have more than one zero. Estimate the zero using 2 iterations of Newton's Method, if the...
For X near ), local linearization gives 1+x. Using a graph, decide if the approximation is an over or underestimate, and estimate to one decimal place the magnitude of the error for -0.9 <x<0.9. typu approximation is an underestimate the absolute tolerance is +/-0.1 Click if you would like to Show Work for this question: Qpen Show Work