 |
|---|
| PAGE: 799 | SET: Exercises | PROBLEM: 15 |
The function is 
and 
, 
, 
(a)
Find the Taylor polynomial with degree 
at the number 
.
Definition of Taylor series:
If a function 
has derivatives of all orders at 
then the series
is called Taylor series for 
at .
First find the successive derivatives of .
Apply derivative on each side with respect to 
.
Find the values of the above functions at 
.
.
.
.
The series is centered at .
Taylor series centered at .
.
.
(b)
The taylors inequality is 
where 
.
Here , and .
Substitute in
in
Hence, 
.
.
.
The value of ,hence the value of should be 
.
The taylors accuracy inequality is 
.
(c)
The value is 
.
Here .
Substitute 
and .
.
Graph :
Graph the function 
.
Observe the graph:
The functions 
for small value of 
in the interval .
(a) .
(b) 
(c)
Graph of the function is
The functions 
for small value of 
in the interval .
|
"I want to tell you that our students did well on the math exam and showed a marked improvement that, in my estimation, reflected the professional development the faculty received from you. THANK YOU!!!" June Barnett |
|
"Your site is amazing! It helped me get through Algebra." Charles |
|
"My daughter uses it to supplement her Algebra 1 school work. She finds it very helpful." Dan Pease |
Simply chose a support option
  
|