Taylor series expression of the function.
$begingroup$
Suppose we are given the following function.
$$f(x)=frac{1}{2}[xsqrt{1-x^2} +sin^{-1}x]$$. Write down the Taylor series expansion about the origin, up to term involving $x^7$, for the function.
This problem was asked in a mathematics exam where students have to solve 40 questions in 150 minutes.
I know the routine method but it is too lengthy.
Is there a more easy("Think out of the box") like approach to solve it.
real-analysis
asked Jan 6 at 13:55
StammeringMathematicianStammeringMathematician
2,3121322
$endgroup$
add a comment |
$begingroup$
Suppose we are given the following function.
$$f(x)=frac{1}{2}[xsqrt{1-x^2} +sin^{-1}x]$$. Write down the Taylor series expansion about the origin, up to term involving $x^7$, for the function.
This problem was asked in a mathematics exam where students have to solve 40 questions in 150 minutes.
I know the routine method but it is too lengthy.
Is there a more easy("Think out of the box") like approach to solve it.
real-analysis
asked Jan 6 at 13:55
StammeringMathematicianStammeringMathematician
2,3121322
$endgroup$
3
$begingroup$
Differentiate it?
$endgroup$
– Lord Shark the Unknown
Jan 6 at 13:58
$begingroup$
Got it. Thanks!!
$endgroup$
– StammeringMathematician
Jan 6 at 13:59
add a comment |
$begingroup$
Suppose we are given the following function.
$$f(x)=frac{1}{2}[xsqrt{1-x^2} +sin^{-1}x]$$. Write down the Taylor series expansion about the origin, up to term involving $x^7$, for the function.
This problem was asked in a mathematics exam where students have to solve 40 questions in 150 minutes.
I know the routine method but it is too lengthy.
Is there a more easy("Think out of the box") like approach to solve it.
real-analysis
asked Jan 6 at 13:55
StammeringMathematicianStammeringMathematician
2,3121322
$endgroup$
Suppose we are given the following function.
$$f(x)=frac{1}{2}[xsqrt{1-x^2} +sin^{-1}x]$$. Write down the Taylor series expansion about the origin, up to term involving $x^7$, for the function.
This problem was asked in a mathematics exam where students have to solve 40 questions in 150 minutes.
I know the routine method but it is too lengthy.
Is there a more easy("Think out of the box") like approach to solve it.
real-analysis
real-analysis
asked Jan 6 at 13:55
StammeringMathematicianStammeringMathematician
2,3121322
asked Jan 6 at 13:55
StammeringMathematicianStammeringMathematician
2,3121322
asked Jan 6 at 13:55
StammeringMathematicianStammeringMathematician
2,3121322
asked Jan 6 at 13:55
StammeringMathematicianStammeringMathematician
2,3121322
asked Jan 6 at 13:55
StammeringMathematicianStammeringMathematician
2,3121322
2,3121322
3
$begingroup$
Differentiate it?
$endgroup$
– Lord Shark the Unknown
Jan 6 at 13:58
$begingroup$
Got it. Thanks!!
$endgroup$
– StammeringMathematician
Jan 6 at 13:59
add a comment |
3
$begingroup$
Differentiate it?
$endgroup$
– Lord Shark the Unknown
Jan 6 at 13:58
$begingroup$
Got it. Thanks!!
$endgroup$
– StammeringMathematician
Jan 6 at 13:59
3
3
$begingroup$
Differentiate it?
$endgroup$
– Lord Shark the Unknown
Jan 6 at 13:58
$begingroup$
Differentiate it?
$endgroup$
– Lord Shark the Unknown
Jan 6 at 13:58
$begingroup$
Got it. Thanks!!
$endgroup$
– StammeringMathematician
Jan 6 at 13:59
$begingroup$
Got it. Thanks!!
$endgroup$
– StammeringMathematician
Jan 6 at 13:59
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
Your function is just$$int_0^xsqrt{1-t^2},mathrm dt.$$
answered Jan 6 at 14:00
José Carlos SantosJosé Carlos Santos
154k22124227
$endgroup$
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Your function is just$$int_0^xsqrt{1-t^2},mathrm dt.$$
answered Jan 6 at 14:00
José Carlos SantosJosé Carlos Santos
154k22124227
$endgroup$
add a comment |
$begingroup$
Your function is just$$int_0^xsqrt{1-t^2},mathrm dt.$$
answered Jan 6 at 14:00
José Carlos SantosJosé Carlos Santos
154k22124227
$endgroup$
add a comment |
$begingroup$
Your function is just$$int_0^xsqrt{1-t^2},mathrm dt.$$
answered Jan 6 at 14:00
José Carlos SantosJosé Carlos Santos
154k22124227
$endgroup$
Your function is just$$int_0^xsqrt{1-t^2},mathrm dt.$$
answered Jan 6 at 14:00
José Carlos SantosJosé Carlos Santos
154k22124227
answered Jan 6 at 14:00
José Carlos SantosJosé Carlos Santos
154k22124227
answered Jan 6 at 14:00
José Carlos SantosJosé Carlos Santos
154k22124227
answered Jan 6 at 14:00
José Carlos SantosJosé Carlos Santos
154k22124227
154k22124227
add a comment |
add a comment |
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3
$begingroup$
Differentiate it?
$endgroup$
– Lord Shark the Unknown
Jan 6 at 13:58
$begingroup$
Got it. Thanks!!
$endgroup$
– StammeringMathematician
Jan 6 at 13:59