1431test2review.pdf - Math 1431 Fall 2019 Test 2 Review Sections 1.2-2.1 1 Find each limit if it exists x2 − 4 a lim x→−2 x 2    1 g lim x 2

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Math 1431 - Fall 2019 Test 2 Review Sections 1.2-2.1 1. Find each limit, if it exists: a. lim x →- 2 x 2 - 4 x + 2 g. lim x 0 x 2 - 1 x b. lim x 0 sin(4 x ) 5 x h. lim x 0 2 sin( x ) cos( x ) 2 x c. lim x 0 4 + x - 2 x i. lim x 0 5 x tan(9 x ) d. lim x 0 1 x +1 - 1 x j. lim x →-∞ x 2 + 2 x 6 - 7 x e. lim x →- 3 x 2 + x - 6 x 2 - 9 k. lim x →∞ x 2 + x - 3 5 - 3 x 2 f. lim x →-∞ x 2 x 4 + x 2 + 2 l. lim x 0 - | x | x ** Also be able to find limits from graphs and other given information. 2. Given f ( x ) = x + 2 x < - 1 0 x = - 1 x 2 - 1 x > - 1 , a. lim x →- 1 - f ( x ) = b. lim x →- 1+ f ( x ) = c. lim x →- 1 f ( x ) = 3. Determine if the following functions are continuous. If the function is continuous, show it by the definition of con- tinuity and if it is not, give the type of discontinuity. a. f ( x ) = x 2 + 1 x < 1 8 x = 1 x 3 x > 1 c. f ( x ) = 5 - x x < - 2 7 x = - 2 x 2 - 5 x > - 2 b. f ( x ) = 2 x 2 x < - 2 8 x = 2 x 3 x > 2 d. f ( x ) = ( x 2 x < - 1 x + 2 x ≥ - 1 1

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4. Let f ( x ) = ( x + 1 x 6 = 3 k x = 3 For what value of k would f ( x ) be continuous at x = 3?
• Spring '16
• Continuous function, c. lim, h. lim, definition of continuity

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