Lab 1 - Zamfir PDF

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MATH 2413: Worksheet 1 Secs%2.2,%2.3%(10%pts)%Write%complete%solutions%for%all%of%the%following%questions.%Show%all%of% your%work/steps;%a%correct%answer%alone%will%not%receive%any%credit.%If%needed%submit%your% paperwork%on%a%separate%sheet%of%paper.% 1.

(3pts)%The%function%ℎ(𝑥 )%is%shown%below.%State%the%value%of%each%limit%shown%below% the%graph.%If%the%limit%doesn’t%exist,%write%“does%not%exist”%and%then%explain%why.%

%

% a.

lim !→# ℎ(𝑥)%=%3%

b.

lim !→$! ℎ(𝑥)%=%1%

c.

lim !→$ ℎ(𝑥)%=%DNE%

d.

ℎ(3)%=%-2%

e.

lim !→%" ℎ(𝑥)%=%DNE%

f. g. 2.

lim !→&%" ℎ(𝑥 )%=%-1%

lim !→&%! ℎ(𝑥 )%=%DNE%

(2%pts)%Sketch%the%graph%of%a%function%𝑓%with%the%given%properties.% –

lim !→&# 𝑓(𝑥) = 5%

–

lim !→$! 𝑓(𝑥) = −3%

–

lim !→$" 𝑓(𝑥) = 2%

–

𝑓 (3)%is%undefined%

% %

% %

%

%

3.

(3%pts)%Compute%the%following%limits%algebraically.%You%may%graph%the%functions%in% Desmos%to%confirm%your%response.%Your%response%will%be%graded%based%on%the% algebraic%computations%performed.% !'$

a.

lim !→&$ ! # '!&(%

b.

lim )→*

c.

lim !→#$

% +&()'%)#

%

)

!&#$ √!'$&+

% %

%

%

% 4.

(2%pts)%Apply%the%Squeeze%Theorem%to%find%the%following%limit.%Use%the%Desmos%link% below%to%visualize%the%functions%used.% https://www.desmos.com/calculator/vhrivozknh% Attach%a%screenshot%of%Desmos%or%show%the%Learning%Assistants%the%graph%to%receive% credit.% 1 lim 𝑥 %cos + -% !→* 𝑥...