
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 30th, 2018, 05:21 PM  #1 
Newbie Joined: Apr 2018 From: The House of My Parents... [like the typicall millennial] Posts: 5 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: 1,974 Thanks: 1025  
May 1st, 2018, 08:47 AM  #3 
Newbie Joined: Apr 2018 From: The House of My Parents... [like the typicall millennial] Posts: 5 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: 2,755 Thanks: 1405 
$\displaystyle \lim_{x \to 0} \dfrac{\tan(kx)}{x}$ $\displaystyle k \cdot \lim_{x \to 0} \dfrac{\tan(kx)}{kx}$ $\displaystyle k \cdot \lim_{x \to 0} \dfrac{1}{\cos(kx)} \cdot \dfrac{\sin(kx)}{kx}$ 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: 5 Thanks: 0 Math Focus: idk... I like everything!  Quote:
 
May 1st, 2018, 10:15 AM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,755 Thanks: 1405  
May 1st, 2018, 10:31 AM  #7 
Newbie Joined: Apr 2018 From: The House of My Parents... [like the typicall millennial] Posts: 5 Thanks: 0 Math Focus: idk... I like everything!  
May 1st, 2018, 10:46 AM  #8  
Senior Member Joined: Sep 2015 From: USA Posts: 1,974 Thanks: 1025  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: 1,797 Thanks: 715 Math Focus: Wibbly wobbly timeywimey stuff.  
May 1st, 2018, 08:25 PM  #10 
Senior Member Joined: Sep 2016 From: USA Posts: 382 Thanks: 205 Math Focus: Dynamical systems, analytic function theory, numerics  

Tags 
calculus, demonstrate, demostration, limits, theorem, trigonometry, urgent 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
I need to demonstrate that this application is surjective  HeiMatau  Algebra  1  January 11th, 2016 11:30 AM 
Demonstrate set equivalence  shunya  Elementary Math  1  December 15th, 2015 06:27 PM 
Can we demonstrate this by contour integral?  stainburg  Complex Analysis  0  November 27th, 2013 10:59 AM 
Demonstrate that a polynomial is a certain Big O value  gretty1  Applied Math  2  July 14th, 2013 11:48 AM 
Demonstrate this  Moonchild  Advanced Statistics  1  October 20th, 2009 01:38 PM 