Transcript CALCULUS AB #6

CALCULUS AB #6
BY: Brown Sugar and ‫אהרון מרקוביץ‬
What
does it
mean?!
1-2sin(x)=e-4x
Plug it In
1-2sin(0)=e-4(0)
1=1
Happy Face
The functions must be
equal—but not necessarily
differentiable—at x=0
Take Some Derivatives!!!!!!!!
When x≤0…
When x>0…
e-4x
1-2sin(x)
DERIVE!
DERIVE!
CHAIN RULE!
-4e-4x
-2cos(x)
-2cos(x)
For x≤0
-4e-4x
For x>0
f(x)=
-2cos(x)=
-3
4 x
444eee44x x 333
-2cos(x)= -3
-2cos(x)= -3 3
cos( x) 
2
 lnlnln44 
 3
-2cos(x)=
 4e444xx4xx -33333 
ln
lnee
 
 4
ln e  4 x  ln  
333 4 
-3

-2cos(x)=


44xx 
 ln



ln


 4 x  ln443
 4 x  ln 4
 1  34
x  11ln33 
xx  4 1ln
-2cos(x)=
-3
43 
ln
x  44 ln44 
4 4
Average
1 Va
Average Value:
4 x
 11  2 sin(x)dx  0 e dx

lue:
1  (1) 
0
1
Average Va
1

1
  1 4 x  
0
D
x  2 cos(x)1   e  

2
4
0 
\Luegasf:
Average
1  Va
  1 4 1  
 2  1  2 cos(1)   e   
lue:
2
4 
 4
1  13
1 4 
  2 cos(1)  e 
2 4
4

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THE END