Difference between revisions of "009A Sample Midterm 1, Problem 3"

Latest revision as of 18:29, 5 November 2017

Consider the following function $f:$

f(x)=\left\{{\begin{array}{lr}x^{2}&{\text{if }}x<1\\{\sqrt {x}}&{\text{if }}x\geq 1\end{array}}\right.

(a) Find $\lim _{x\rightarrow 1^{-}}f(x).$

(b) Find $\lim _{x\rightarrow 1^{+}}f(x).$

(c) Find $\lim _{x\rightarrow 1}f(x).$

(d) Is $f$ continuous at $x=1?$ Briefly explain.

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 <span class="exam">(d) Is &nbsp;<math style="vertical-align: -5px">f</math>&nbsp; continuous at &nbsp;<math style="vertical-align: -1px">x=1?</math>&nbsp; Briefly explain.
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+[[009A Sample Midterm 1, Problem 3 Detailed Solution|'''<u>Detailed Solution with Background Information</u>''']]
 [[File:9ASM1P3.jpg|600px|thumb|center]]
-[[009A Sample Midterm 1, Problem 3 Detailed Solution|'''<u>Detailed Solution for this Problem</u>''']]
 [[009A_Sample_Midterm_1|'''<u>Return to Sample Exam</u>''']]