a.
The linear approximation to the given function at the point a = 0
is given by the linear function L :
defined by,
L(x) = f(0) + f'(0)x. Now, the derivative of f at 0 is
2e0 = 2.
Thus, the equation of the line that represents the linear
approximation to the function f at a = 0 is
L(x) = 2 + 2x.
b.
Now, f(0.03)
L(0.03) = 2 + 2 x 0.03 = 2.06
c.
With the aid of a calculator, f(0.03) = 2e0.03 =
2.06091
Thus, the percent error in the approximation is given by,
a. Write the equation of the line that represents the linear approximation to the following function...
write the equation of the line that represents the
linear approximation to the following function at the given point
a. answer a, b and c.
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) =...
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 Japproximation - exact| c. Compute the percent error in the approximation, 100.- exact where the exact value is given by a calculator. f(x) = (729 + x) 9; a = 0; f(0.1) a. L(x)= b. Using the linear approximation, f(0.1) | (Round to the nearest hundredth as needed.) c....
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)=4eat a0; (0.03)
a. Write the equation of the line that represents the linear
approximation to the following function at the given point a.
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 -0.04 f(x) = 3 e -*;...
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=?
a. Find the linear approximation for the following function at the given point. b. Use part (a) to estimate the given function value. f(x,y) = 3x - 2y + 8xy; (3,5); estimate f(2.9,5.02) a. L(x,y)= b. L(2.9,5.02) = (Type an integer or a decimal.)
1)
2)
3)
Use linear approximation, i.e. the tangent line, to approximate 15.22 as follows: Let f(x) = z² and find the equation of the tangent line to f(x) at x = 15. Using this, find your approximation for 15.22 Given the function below f(x) = -180x3 + 396 1. Answer in mx + b form. Find the equation of the tangent line to the graph of the function at x = L(2) Use the tangent line to approximate f(1.1)....
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...
Given the function below f(x) = 3 – 45x3 + 72 Find the equation of the tangent line to the graph of the function at x = 1. Answer in mx + b form. L(x) Use the tangent line to approximate f(1.1). L(1.1) Compute the actual value of f(1.1). What is the error between the function value and the linear approximation? Answer as a positive value only. error (Approximate to at least 5 decimal places.)
a. Use the given Taylor polynomial p, to approximate the given quantity b. Compute the absolute error in the approximation assuming the exact value is given by a calculator Approximate e-004 using f(x) = -* and p(x) = 1 -x+ a. Using the Taylor polynomialpy.c-004 (Do not round until the final answer. Then round to four decimal places as needed.) b. absolute error (Uso scientific notation. Use the multiplication symbol in the math palette as needed. Round to two decimal...