# 1 3 g x g 0 g 0 x 0 1 x 1 x 3 1 3 1 x 1 3 1 005 0983

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1 = g ( x ) g (0) + g' (0)( x 0) = 1 + x . 1 + x 1 + x 1 = = 1 + ( 0.05) = 0.983 0.95 3 1 + ( 0.05) 3 = = 1 + (0.1) = 1.033 . 1.1 3 1 + 0.1 3 3 3 1 3 3 1 3 1 3
12/14/16, 3)58 PM hw18S3.10 Graphing f and the tangent line we have: 7. 4/4 points | Previous Answers SCalcET7 3.10.005. Find the linear approximation of the function at a = 0. Use L ( x ) to approximate the numbers (Round your answers to four decimal places.) x
Page 6 of 11 Illustrate by graphing f and the tangent line.
12/14/16, 3)58 PM hw18S3.10 Page 7 of 11 Solution or Explanation so and Therefore, The linear approximation to f at x = 0 provides a good approximation to f for x near 0, so and f ( x ) = f ' ( x ) = , 4 x 1 2 4 x f (0) = 2 f ' (0) = . 1 4 = f ( x ) f (0) + f ' (0)( x 0) = 2 + ( x 0) = 2 x . 4 x 1 4 1 4 2 x 1 4 = f (0.1) = 1.975 3.9 4 0.1 1 4
12/14/16, 3)58 PM hw18S3.10 Page 8 of 11 Graphing f and the tangent line we have: 8. 3/3 points | Previous Answers (Old Final Exam Problem-A2011) A right circular cone of height h and base radius r has total surface area S consisting of its base area plus its side area, leading to the formula: S = π Suppose you start out with a cone of height 8 cm and base radius 6 cm, and you want to change the dimensions in such a way that the total surface area remains the same. Suppose you increase the height by 54 /100. In this problem, use tangent line approximation to estimate the new value of r so that the new cone has the same total surface area. The estimated value of r r 2 + r r 2 + h 2 π = \$\$5.899 = f (0.01) = 1.9975 . 3.99 4 0.01 1 4
12/14/16, 3)58 PM hw18S3.10 Page 9 of 11 9. 3/3 points | Previous Answers A sphere of radius 3 inches is sliced with two parallel planes: one passes through the equator and the other is H inches above the first plane. The resulting portion of the sphere between the two planes is called a spherical segment ; see the picture: In Math 125, you will show that the volume V