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April 30th, 2018, 05:21 PM  #1 
Newbie Joined: Apr 2018 From: The House of My Parents... [like the typicall millennial] Posts: 6 Thanks: 0 Math Focus: idk... I like everything!  Can you help me to demonstrate these limits? [It's URGENT!!!!]
Hello! Thank you for bothering to help me with this.... I need you to please help me with these points of my calculus activity. The subject is called Trigonometric Limits. The first one [A] has to be demonstrated using the sandwich theorem. And the second [F] has to be demonstrated as you would normally do. Please show me step by step how you would do it.... Thank you in advance for your help. 
April 30th, 2018, 05:41 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,037 Thanks: 1063  
May 1st, 2018, 08:47 AM  #3 
Newbie Joined: Apr 2018 From: The House of My Parents... [like the typicall millennial] Posts: 6 Thanks: 0 Math Focus: idk... I like everything! 
Thank you very much for the first exercise.... It really helped. But you could give me a hand with the second one, because I think they look a little different from each other. I'd really appreciate your help, buddy....

May 1st, 2018, 09:09 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,761 Thanks: 1416 
$\displaystyle \lim_{x \to 0} \dfrac{\tan(kx)}{x}$ $\displaystyle k \cdot \lim_{x \to 0} \dfrac{\tan(kx)}{kx}$ $\displaystyle k \cdot \lim_{x \to 0} \dfrac{1}{\cos(kx)} \cdot \dfrac{\sin(kx)}{kx}$ let $y = kx$ $x \to 0 \implies y \to 0$ ... $\displaystyle k \cdot \lim_{y \to 0} \dfrac{1}{\cos(y)} \cdot \dfrac{\sin(y)}{y}$ can you finish? 
May 1st, 2018, 09:59 AM  #5  
Newbie Joined: Apr 2018 From: The House of My Parents... [like the typicall millennial] Posts: 6 Thanks: 0 Math Focus: idk... I like everything!  Quote:
 
May 1st, 2018, 10:15 AM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,761 Thanks: 1416  
May 1st, 2018, 10:31 AM  #7 
Newbie Joined: Apr 2018 From: The House of My Parents... [like the typicall millennial] Posts: 6 Thanks: 0 Math Focus: idk... I like everything!  
May 1st, 2018, 10:46 AM  #8  
Senior Member Joined: Sep 2015 From: USA Posts: 2,037 Thanks: 1063  Quote:
Take the last line of Skeeter's post at 10:09 you know what $\lim \limits_{y \to 0} \dfrac{\sin(y)}{y}$ is you copied it from that website to show it's $1$ now you have a factor of $k \dfrac {1}{\cos(y)}$ left just plug in the 0 and read it off, the denominator doesn't blow up.  
May 1st, 2018, 07:22 PM  #9 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,852 Thanks: 749 Math Focus: Wibbly wobbly timeywimey stuff.  
May 1st, 2018, 08:25 PM  #10 
Senior Member Joined: Sep 2016 From: USA Posts: 413 Thanks: 227 Math Focus: Dynamical systems, analytic function theory, numerics  

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calculus, demonstrate, demostration, limits, theorem, trigonometry, urgent 
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