Exam 1: Limits and Continuity

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Let Let   , find  , find Let   , find

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C

Answer true or false. Answer true or false.   is equivalent to  is equivalent to Answer true or false.   is equivalent to

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For the function f graphed here: For the function f graphed here:   find   . find For the function f graphed here:   find   . .

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It does not exist.

Consider the function f graphed here: Consider the function f graphed here:   For what values of a does   not exist? For what values of a does Consider the function f graphed here:   For what values of a does   not exist? not exist?

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Find Find   . .

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Use Use   and   to prove   . and Use   and   to prove   . to prove Use   and   to prove   . .

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Answer true or false. Answer true or false.

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For the function h graphed here For the function h graphed here   find  find For the function h graphed here   find

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Answer true or false. It is possible to show that Answer true or false. It is possible to show that   . .

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Find Find   . .

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Prove that Prove that   . .

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Answer true or false. f(x) = |x2 - 4| has points of discontinuity at x = -2 and x = 2.

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Find Find   . .

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Find a value for the constant k so that  Find a value for the constant k so that   will be continuous at  \theta   = 0. will be continuous at θ\theta = 0.

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For the function f graphed here: For the function f graphed here:   find  find For the function f graphed here:   find

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For the function f graphed here: For the function f graphed here:   find  find For the function f graphed here:   find

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Find Find   . .

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If  If   and  \varepsilon  = 0.0368, find a smallest positive number  \delta   such that |f(x) - 16| < 0.0368 if 0 < |x - 4| <  \delta  . and ε\varepsilon = 0.0368, find a smallest positive number δ\delta such that |f(x) - 16| < 0.0368 if 0 < |x - 4| < δ\delta .

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Show that Show that   cannot be made continuous for any assigned value of the constant k. cannot be made continuous for any assigned value of the constant k.

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Let Let   . Find   . . Find Let   . Find   . .

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