Calculus/Limits/Solutions

One-Sided Limits

Evaluate the following limits or state that the limit does not exist. Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer

Two-Sided Limits

Evaluate the following limits or state that the limit does not exist. Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer

Limits to Infinity

Evaluate the following limits or state that the limit does not exist. Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer

Limits of Piecewise Functions

Evaluate the following limits or state that the limit does not exist.

48. Consider the function

$f(x)=\{\begin{array}{cc}(x-2{)}^2& \text{if }x<2\\ x-3& \text{if }x\ge 2.\end{array}$

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49. Consider the function

$g(x)=\{\begin{array}{cc}-2x+1& \text{if }x\le 0\\ x+1& \text{if }0<x<4\\ x^2+2& \text{if }x\ge 4.\end{array}$

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50. Consider the function

$h(x)=\{\begin{array}{cc}2x-3& \text{if }x<2\\ 8& \text{if }x=2\\ -x+3& \text{if }x>2.\end{array}$

Intermediate Value Theorem

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