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Lecture 14 :Linear Approximations and Differentials. Consider a point on a smooth curve y = f(x), say P = (a, f(a)), If we draw a tangent line to the curve at the point P, we can see from the pictures below that as we zoom in towards the point P, the path of the curve is very close to that of the tangent line. If we zoom in far
Worksheet # 22: Linear Approximation. 1. For each of the following, use a linear approximation to estimate the actual value. (a) tan(44?). (b) (3.01)3. (c). v. 17. (d) 8.062/3. 2. Suppose we want to paint a sphere of radius 200 cm with a coat of paint .2 cm thick. Use a linearization to approximate the amount of paint we need to
AP Calculus AB - Worksheet 24. Linear Approximations. 1. If f x( )= x3 + 3x, approximate f 2.01. ( ) using linearization. 2. For the function f, f ' = 2x +1 and f 1( )= 4 . What is the approximation for f 1.2. ( ) using the tangent line approximation? 3. Approximate 24.9 + 24.9. ( )2 using linearization. 4. Find an approximate value for f
MATH 1170. Section 3.9 Worksheet. NAME. Linear Approximations and Differentials. Linearizations. The idea behind linear approximations is that it might be easy to calculate the value f(a) for some a but difficult to compute the value f(x) for some x near a. But before we figure out how to do this, let's review a couple of points
The approximation f (x) % L(x) is the standard linear approximation of f at a. The point .r = a is the center of the approximation. EXAMPLE 1 Finding a Linearization. Find the linearization of f (x) I V l + x at x = O, and use it to approximate. 1.02 without a calculator. Then use a calculator to determine the accuracy of the.
+. This means that ( ) ( ) ( ). ' f a h. f a. f a h. +. + . This approximation is called a linear approximation or a linear tangent approximation. This is often written: (. ) ( ) ( ) Worksheet 1. 1. Without the use of a calculator find the approximate value of a) ( ). 1. 3. 8.02 b) sin31°. (note 1. 0.01745. ° = radians) c) ( )1.5. 4.1 d) 3 0.126. 2.
Worksheet 17: Linear Approximation & Differentials. Russell Buehler. b.r@berkeley.edu www.xkcd.com. 1. Find the linearization of f(x) = sin(x) at a = ?. 2 . Taking the derivative, f (x) = cos(x), so f (a) = f (?. 2. ) = 0. Thus the linearizion. (tangent line at a) is L(x) = f(a) + 0(x - a) = sin(?. 2. )+0=1. 2. Find the linearization of f(x) = x.
Calculus and Analytic Geometry 1. Fall 2006. Name: Worksheet #6 - Linear Approximation. In this worksheet, you will use linear approximations to estimate values of functions and solutions of equations. 1 Let F(x) = x. 1. 5 . Estimate F(32.1) by using a linear approximation at x = 32. 2 Use a linear approximation to estimate
Math 1a. §3.8 Worksheet. Linear Approximations and Differentials. Fall 2005. 1. Estimate v101 without using your calculator. How does this compare to the answer that you obtain from your calculator. 2. Estimate v98 without using your calculator. How does this compare to the answer that you obtain from your calculator. 1
Worksheet # 17: Linear Approximation and Applications. 1. For each of the following, use a linear approximation to the change in the function and a convenient nearby point to estimate the value: (a) (3.01)3. (b). /. 17. (c) 8.062/3. (d) tan(44?). 2. What is the relation between the linearization of a function f(x) at x = a and the
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