Exam 1: Limits and Continuity

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

(Short Answer)
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If  If   and  \varepsilon  = 0.006, find a largest positive number  \delta   such that |f(x) - 5| < 0.006 if 0 < |x - 4| <  \delta  . (Round to 3 decimal places.) and ε\varepsilon = 0.006, find a largest positive number δ\delta such that |f(x) - 5| < 0.006 if 0 < |x - 4| < δ\delta . (Round to 3 decimal places.)

(Multiple Choice)
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Find Find   . .

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Find Find   . .

(Essay)
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Find Find   . .

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Answer true or false. Answer true or false.

(True/False)
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Prove that  Prove that   is continuous on [0,+ \infty ). is continuous on [0,+ \infty ).

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For the function g graphed here: For the function g graphed here:   find  find For the function g graphed here:   find

(Short Answer)
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Answer true or false. Answer true or false.

(True/False)
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Assign a value to the constant k which will make f continuous. Assign a value to the constant k which will make f continuous.

(Essay)
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Find Find   . .

(Short Answer)
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Find the limit. Find the limit.

(Multiple Choice)
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Find the x-coordinates for all points of discontinuity for Find the x-coordinates for all points of discontinuity for   . .

(Multiple Choice)
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Find Find   . .

(Essay)
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Find Find   . .

(Essay)
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Use the substitution  Use the substitution   to express the limit as an equivalent limit in which t  \rightarrow  0<sup>+</sup>.   to express the limit as an equivalent limit in which t \rightarrow 0+.  Use the substitution   to express the limit as an equivalent limit in which t  \rightarrow  0<sup>+</sup>.

(Essay)
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Find Find   . .

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Answer true or false. f(x) = tan (x4 - 1) has no point of discontinuity.

(True/False)
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Find the left hand limit at x = 4 for Find the left hand limit at x = 4 for   . .

(Essay)
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Answer true or false. The value of k that makes f continuous for Answer true or false. The value of k that makes f continuous for   is 7 is 7

(True/False)
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