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3_9_differentials

# 3_9_differentials - 3.9 Differentials Definition Let y =...

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Unformatted text preview: 3.9 Differentials Definition: Let y = f(x) represent a function that is differentiable on an open interval containing x. The differential of x (dx) is any nonzero real number. The differential of y (dy) is: dy = f ' (x) dx Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework on Web Part 1 Part 2 Title: Differentials (1 of 5) Estimate 6 Estimate 5 One method is to use the tangent line . This can be a good estimate when the value of x is close to a value that is easy to compute. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework on Web Part 1 Part 2 Title: Estimate w Tangent (2 of 5) Another method is to use differentials: Find 5 Use y = x . Let x = 4 and dx =+1 dy = f '(x) dx dy = 1/(2x) dx dy = 1/(24) (1) dy = 1/4 Therefore, 5 = 4 + dy = 2 + 1/4 = 2.25 Calculator ~ 2.24 Calculus Home Page Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework on Web Part 1 Part 2 Title: Estimate w differentials (3 of 5) Title: Example 1 (4 of 5) 3.9 Differentials 3.9 # 1, 715, 19, 27, 31, 37, 41 Homework on the Web Part 1 Part 2 Calculus Home Page Class Notes: Prof. G. Battaly, Westchester Community College, NY Title: Homework (5 of 5) ...
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