Exam 1: Limits and Continuity

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Find the limit. Find the limit.

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Answer true or false. Answer true or false.

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Find any points of discontinuity for Find any points of discontinuity for   . .

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Find the limit Find the limit

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Approximate the limit by evaluating Approximate the limit by evaluating   at appropriate values of x.  at appropriate values of x. Approximate the limit by evaluating   at appropriate values of x.

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

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Given Given   , determine if h is continuous at -6. , determine if h is continuous at -6.

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Answer true or false. To use a δ\delta - ε\varepsilon approach to show that  Answer true or false. To use a  \delta  - \varepsilon  approach to show that   , a reasonable first step would be to change the limit to   . , a reasonable first step would be to change the limit to  Answer true or false. To use a  \delta  - \varepsilon  approach to show that   , a reasonable first step would be to change the limit to   . .

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A point of discontinuity of A point of discontinuity of   is at is at

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Find Find   . .

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Find Find   . .

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Answer true or false. f(x) = x2 - 6x + 5 = 0 has at least one solution on the interval [0, 2].

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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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Find Find   where   . where Find   where   . .

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For the function graphed here For the function graphed here   Find   . Find For the function graphed here   Find   . .

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Answer true or false. The Squeeze Theorem can be used to show Answer true or false. The Squeeze Theorem can be used to show   utilizing   and   . utilizing Answer true or false. The Squeeze Theorem can be used to show   utilizing   and   . and Answer true or false. The Squeeze Theorem can be used to show   utilizing   and   . .

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Show that Show that   is not continuous at x = -6 but is continuous from the right at x = -6. is not continuous at x = -6 but is continuous from the right at x = -6.

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Prove that Prove that   . .

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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 t = 0. will be continuous at t = 0.

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Find Find   . .

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