1)What is linear approximation used for? Why would you use the linear approximat

Question

1)What is linear approximation used for? Why would you use the linear approximation of a function rather than the actual function? 1b.) State the general formula for La(x), the linear approximation of a function around the point x = a. Use this formula to find the linear approximation Lo(x) of the function f(x) =root 1 - x at a = 0. 1c.) Use the linear approximation that you found in part (b) to approximate root 0.99. 1d.) Use your calculator to find the actual value of root 0.99 correct to 5 decimal places? 1e)Sketch and label the graphs of both f(x) and Lo(x) and label the point where they touch. Use these graphs to determine if your estimate in part (1f) is greater or less than the actual value of root 0.99. Explain your choice by referring to the graphs of f(x) and Lo(x).(IF YOU SEE A ?, IT REALLY MEANS (-) MINUS SIGN

Explanation / Answer

Inmathematics, alinear approximationis an approximation of a generalfunctionusing alinear function(more precisely, anaffine function). They are widely used in the method offinite differencesto produce first order methods for solving or approximating solutions to equations.

for better understanding of linear approximations go through

http://en.wikipedia.org/wiki/Linear_approximation

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