1024worksheet4

# 1024worksheet4 - fail to be continuous(h For what values of...

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Polytechnic Institute of NYU MA 1024/1324 Worksheet 4 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 12 2 12 3 12 4 12 5 14 6 14 7 12 8 12 Total 100 1

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2 (1) Are the functions continuous on the given intervals? (a) f ( x ) = x 2 2 + x - 4 on [ e,π ] (b) f ( x ) = 1 2 x - 7 on [4 , 5] (c) f ( x ) = e sin x cos x on h - π 6 , π 6 i
3 (2) Sketch the graph and ﬁnd the discontinuities of the following functions (if any). (a) g ( x ) = x - 3 x 2 - 9 (b) h ( x ) = 1 , x < 0 x 2 , 0 < x < 1 1 , 1 x < 3 x, 3 x.

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4 (3) Find the discontinuities of the following functions(if any). (a) h ( x ) = x 2 - 16 x - 4 (b) g ( x ) = | x - 2 | (c) f ( x ) = - 1 , x < - 1 x 3 , - 1 x 1 1 , 1 < x
5 (4) Calculate the exact value of the following limits, or write DNE if it does not exist. (a) lim x 2 | x - 2 | x - 2 (b) lim x 6 - | x - 6 | x - 6 (c) lim x 6 3 x 2 - 19 x + 6 x - 6 (d) lim x →∞ 2 e - x + 3 3 e - x + 2

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6 (5) Given the function f ( x ) as the following ﬁgure: Determine the following (if it exists): (a) lim x →- 1 f ( x ) = (b) f ( - 1) = (c) lim x 1 f ( x ) = (d) f (1) = (e) lim x 3 f ( x ) = (f) f (3) = (g) For what values of x does f ( x

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Unformatted text preview: ) fail to be continuous? (h) For what values of x does the derivative do not exist? 7 (6) Given the function g ( x ) as the following ﬁgure: Determine the following (if it exists): (a) lim x →-2 g ( x ) (b) lim x → g ( x ) (c) g (0) (d) lim x → 2-g ( x ) (e) lim x → 2 + g ( x ) (f) g (2) (g) For what values of x does g ( x ) fail to be continuous? (h) For what values of x does the derivative do not exist? 8 (7) Find f (2) by using the limit deﬁnition of the derivative at a point. (a) f ( x ) = (3 x-7) 2 (b) f ( x ) = 9 x + 4 (c) f ( x ) = x + √ 2 x 9 (8) Find the points where the derivative does not exist. (a) f ( x ) = | 2 x-5 | (b) f ( x ) = | x 2-4 | (c) f ( x ) = ± x 2 , x ≤ 1 2-x, x > 1 (d) f ( x ) = ± x 3-1 , x ≤ 2 3 , x > 2...
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1024worksheet4 - fail to be continuous(h For what values of...

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