00:01
In this problem, the first question is to determine the mclorean series expansion of tan inverse of 4x and write the first five terms.
00:08
We know that the mclorean series expansion of tan inverse of x's summation n ranging from 0 to infinity, negative on the whole raise to n times x raised to 2n plus 1 divided by 2n plus 1.
00:22
Now the mcluhan series expansion of tan inverse of 4x can be obtained by replacing all occurrences of x in.
00:30
This mcluhan series expansion with 4x therefore it is summation and ranging from 0 to infinity negative on the whole raise to n times 4x the whole raise to 2n plus 1 divided by 2n plus 1 therefore it is summation n ranging from 0 to infinity negative on the whole raise to n times 4 to 2n plus 1 divided by 2 n plus 1 times x raised to 2n plus 1 therefore writing out the first five terms, this is 4x minus 4 cube by 3 times x cube plus 4 raise to 5 by 5 times x raised to 5 minus 4 raise to 7 divided by 7 times x raised to 7 plus 4 raise to 9 divided by 9 x raised to 9 minus etc.
01:28
Therefore, this is 4x minus 64 by 3x cube plus 1224 by 5 x rays to 5 minus 16 ,384 divided by 7 x rays to 7 plus 262 ,1144 divided by 9 x rays to 9 minus etc.
01:56
And this is the required mclorian series expansion of tan inverse of 4x.
02:03
The second question is to determine the mcluhan series expansion of x cos x cube.
02:11
Now the mcluhan series expansion of cause x is summation n ranging from 0 to infinity, negative on the whole raise to n, x raised to 2n divided by 2n factorial.
02:24
Therefore, the mcluhan series expansion of cause x cubis, summation n ranging from 0 to infinity, negative on the whole raise to n times x cube the whole raise to 2n divided by 2n factorial...