Hw3-31 - Homework 3/31 Part 1 1 Use differentials to approximate(2.002)5 2 Use differentials to approximate(1.997)5 3 Use differentials to

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Unformatted text preview: Homework 3/31 Part 1: 1. Use differentials to approximate (2.002)5 . 2. Use differentials to approximate (1.997)5 . 3. Use differentials to approximate (2 + h)5 . 4. Use differentials to approximate (x)5 near x = 2. NOTE: Your answer to this problem is called the linearization of x5 at x = 2. 5. Graph y = x5 and the linearization at x = 2 on the same axes. Your graph must extend at least from x = 0 to x = 3. 6. Use your linearization to solve x5 = 35. 7. Use your calculator to solve x5 = 35. Part 2: Warning!. Work this problem in radians! 1. Use differentials to approximate tan 46◦ . [Hint: Convert ∆x = 1◦ to radians.] 2. Use differentials to approximate tan 44◦ . 3. Use differentials to approximate tan(π/4 + h). 4. Use differentials to approximate tan x near x = π/4. Simplify your answer. NOTE: Your answer to this problem is called the linearization of tan x at x = π/4. 5. Graph y = tan x and your answer to part (4) on the same axes. Your graph must extend at least from x = 0 to x = π/2. 6. Use your linearization to solve tan x = 5/6. 7. Use your calculator to solve tan x = 5/6. Part 3: Suppose that f (x) = x + sin x − 0.2e0.1x . 1. Find the linearization of f (x) at x = 1. 2. Use your linearization to find a root of f . (That is, solve f (x) = 0.) 1 3. Find the linearization of f (x) at x = 0. 4. Use your linearization to find a root of f . 5. If possible, use your calculator to solve f (x) = 0. Answers Part 1: 1) 32.16; 2) 31.76; 3) 32 + 80h; 4) 32 + 80(x − 2); 6) x = 2 + 3/80 ≈ 2.0375; 7) x ≈ 2.0362. Part 2: 1) 1 + π/90; 2) 1 − π/90; 3) 1 + 2h; 4) 1 + 2(x − π/4); 6) x = π/4 − 1/12 ≈ 0.7021; 7) x = arctan(5/6) ≈ 0.6947. Part 3: 1) f (x) ≈ (1 + sin 1 − 0.2e0.1 ) + (1 + cos 1 − 0.02e0.1 )(x − 1) ≈ 1.620 + 1.518(x − 1). 1 + sin 1 − 0.2e0.1 ≈ −0.0673. 2) x ≈ 1 − 1 + cos 1 − 0.02e0.1 3) f (x) ≈ −0.2 + 1.98x. .2 4) x ≈ ≈ 0.101. 1.98 5) x ≈ 0.1011. 2 ...
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This note was uploaded on 10/12/2011 for the course MATH 170 taught by Professor Staff during the Spring '08 term at Boise State.

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Hw3-31 - Homework 3/31 Part 1 1 Use differentials to approximate(2.002)5 2 Use differentials to approximate(1.997)5 3 Use differentials to

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