FIND THE ANSWERS

First three terms in expansion of (1 − 2x)2(1 + ax)6, in ascending powers of x, are 1 − x + bx2. Find a and b?

Answer this question

  • First three terms in expansion of (1 − 2x)2(1 + ax)6, in ascending powers of x, are 1 − x + bx2. Find a and b?


Answers

Answer #1 | 07/02 2014 06:13
a = 1/2; b = - 17/4 f(x) = (1 − 2x)^2(1 + ax)^6 f '(x) = 2( -2) (1 - 2x) (1 + ax)^6 + (1 − 2x)^2 6a(1 + ax)^5 = = 2(1 - 2x)(1 + ax)^5 ( -2(1 + ax) + 3a(1 - 2x) ) = f '(x) = 2 (2 x - 1) (8 a x - 3 a + 2) (a x + 1)^5 f ''(x) = 2 (112 a^2 x^2 + 28 a x (2 - 3 a) + 15 a^2 - 24 a + 4) (a x + 1)^4 f(0) = 1 f '(0) = 2 (3 a - 2) f ''(0) = 2 (15 a^2 - 24 a + 4) Taylor expansion is 1 + 2x(3a - 2) + x^2 (15a^2 - 24a + 4) coefficient of x is 2(3a - 2) = - 1 a = 1/2 plug in the coefficient of x^2 15(1/2)^2 - 24(1/2) + 4 = - 17/4
Positive: 45 %
Answer #2 | 07/02 2014 05:55
First three terms in expansion of (1 - 2x)^2(1 + ax)^6, in ascending powers of x, are 1 - x + bx2. 1 - 4x + 4x^2 b = 4 Find a and b
Positive: 39 %

Possible answer

in ascending powers of x are I + ax + bx2 ... By using the binomial expansion, or otherwise, find the values Of ... (1 4- 2x) I + ax + bx2 4- 4- 16x where ...
Read more
Positive: 45 %
Core Mathematics C2 Advanced Subsidiary Binomial Expansion ... 1. Find the first three terms, in ascending ... x2 is 6 times the coefficient of x, (b) ...
Read more
Positive: 40 %
... 336 (iii) 7920 (iv) 2n(2n + 1)] 2. Expand: (i) (x + y)6 (ii) (2x ... bx2, find the value of . a, and of . b. ... in ascending powers of x, the first ...
Read more
Positive: 26 %
Find the first three terms, in ascending powers of x, in the expansion of ( 1 ... 5. find the first three terms, in ascending powers of ...
Read more
Positive: 3 %

Show more results