a. Write the equation of the line that represents the linear approximation to the following function...
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=?
Homework Answers
Add Answer to:
a. Write the equation of the line that represents the linear
approximation to the following function...
a. Write the equation of the line that represents the linear approximation to the following function...
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...
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)
write the equation of the line that represents the linear approximation to the following function at...
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...
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. Write the equation of the line that represents the linear approximation to the following function...
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....
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 wan...
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...
1) 2) 3) Use linear approximation, i.e. the tangent line, to approximate 15.22 as follows: Let...
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 Approximations. a. (40 pts) Find the linear approximation L(x) to the function f(x)tan(rx) at a (20 pts) Use the linear approximation to determinethe value at x = 0.4 at χ = 0.4, Comput...
1. Linear Approximations. a. (40 pts) Find the linear approximation L(x) to the function f(x)tan(rx) at a (20 pts) Use the linear approximation to determinethe value at x = 0.4 at χ = 0.4, Compute the relative error: Then compare f(x) and L(x) LLarrul × 100% 1f(x)1 r(x)l
1. Linear Approximations. a. (40 pts) Find the linear approximation L(x) to the function f(x)tan(rx) at a (20 pts) Use the linear approximation to determinethe value at x = 0.4 at χ...
(a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the linear approximation for f(x) around a = e and use this to approx- dy Hence, e T,y 5...
(a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the linear approximation for f(x) around a = e and use this to approx- dy Hence, e T,y 5 marks imate f(3). markS (b) Evaluate the following limits. Simplify your results if possible. 5 marks 5 marks] lim cot 5x sin 6x cos 7a (i) (ii) limIn
(a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the...
I need the error in percentage (6 points) Estimate Af using the Linear Approximation and use...
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:
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 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)
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. 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. 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....
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...
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 Approximations. a. (40 pts) Find the linear approximation L(x) to the function f(x)tan(rx) at a (20 pts) Use the linear approximation to determinethe value at x = 0.4 at χ = 0.4, Compute the relative error: Then compare f(x) and L(x) LLarrul × 100% 1f(x)1 r(x)l
1. Linear Approximations. a. (40 pts) Find the linear approximation L(x) to the function f(x)tan(rx) at a (20 pts) Use the linear approximation to determinethe value at x = 0.4 at χ...
(a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the linear approximation for f(x) around a = e and use this to approx- dy Hence, e T,y 5 marks imate f(3). markS (b) Evaluate the following limits. Simplify your results if possible. 5 marks 5 marks] lim cot 5x sin 6x cos 7a (i) (ii) limIn
(a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the...
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:
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