Calc1131W3T4 - The pinching theorem

Friday, 23 March 2018

1:28 PM

Machine generated alternative text:
f (r) lim h(t) L
Machine generated alternative text:
Il g(z) = cos(z) let's use the ptrrtungtheorantohnd lim g(z) 
We know that for all 
It we muttoly this Inequality by 
Let f(x) 
• lim f(x) 
lim h (r) — 
. g(z) h(x) tor all 
We conclude by ttw pinching theorem that 
O then becomes 
•S cos(r) •S 
4 
lim cos(z) — 
0 
0
Machine generated alternative text:
In compute using the pinching theorem. up to you and With an-d = 
Dul some choices are Dever than ctnery Find suitable runctions f(x) and h(r) 'cr tne 'unctions g(r) listed below. 
Remember to ensure that f(r) g(r) anc g(x) h(zb 
eos(x) 
I e¯3z sin(x) 
Hence Dy me pincning tneorem 
sin (r) ¯ 
lim I e ¯ 
Note: me Maple syntax ror is 
These unique,
Machine generated alternative text:
Lets move that O 
Let D 11,01 and B a centre A 10,01 Let C B the AD. and let t the angle / BAD in radans. as shown 
. The can as 
. The me BD expressec term t as 
By compart" these we get 
tru'n the theorem 
Note the 
(we require lengths to be zero. so use an
Machine generated alternative text:
ters •n 
(m tJr 
o 
02 OA 08 OS 
• • except t

 

Created with Microsoft OneNote 2016.