Quiz 5 (Prequiz) Limits - Calculus PreQuiz 5 - Limits...

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Unformatted text preview: Calculus PreQuiz 5 - Limits Objectives:: You will be able to determine limits with an algebraic approach and limit laws You will be able to evaluate limits with an algebraic approach by simplifying. You will be able to determine limits using the squeeze theorem You will be able to determine the limits of trigonometric functions You will be able to evaluate one-sided limits You will be able to describe the continuity of a function. You will be able to locate and describe the discontinuities of a function Name___________________________________ Date____________________ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Determine the limit algebraically, if it exists. 1) lim x2 x - 3 2) lim x -7 x2 + 11x + 28 x + 7 3) lim x4 x2 + 4x - 32 x2 - 16 6 sin x 7x 4) lim x0 Sandwich Theorem 5) It can be shown that the inequalities 1 -x x cos( ) x x 1 hold for all values of x 0. Find lim x cos( ) if it exists x x0 6) If x3 f(x) x for x in [-1,1], find lim f(x) if it exists. x0 Find the limit. 7) lim 5t cot t t/2 sin x lim x0 7x tan 4 lim 0 sin 5 8) 9) 1 Find the indicated limit. 7x 10) lim x x0 + 11x lim x x0 - 11) Find the points of discontinuity. Identify each type of discontinuity. x + 4 12) y = 2 - 14x + 48 x 13) y = 4x + 5 Find all points where the function is discontinuous. 0, x< 0 14) f(x) = x2 - 4x, 0 x 4 4, 15) x > 4 16) f(x) = x2 - 4 , x + 2 x -2 x = -2 4, 2 Answer Key Testname: QUIZ 5 (PREQUIZ) LIMITS 1) Does not exist 2) -3 3 3) 2 4) 6 7 5) 0 6) 0 7) 0 1 8) 7 9) 4 5 10) 7 11) -11 12) x = 6, x = 8, both infinite discontinuities 5 13) x < - , all points not in the domain 4 14) x = 4 15) x = 1 16) x = -2 3 ...
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