The Student Room Group
Reply 1
anyone?

i can put the answers up and then u mit be able to tell me how to get to them?
Reply 2
ryan750
state the range of values for which the expansions of functions below are valid:

(6 - 11x + 10x^2)/(1+x)(1-2x)^2

(16 - x)/(2-x)(3+x^2)

(16 +y)^1/2

can sum1 explain how they got to their answers please


The expansion of (1+ax)^n where n is not a positive integer, is only valid for :

|ax| < 1 i.e -1 < ax < 1

so the answers to these exercises are the bisections of the flowing sets

1) -1 < x < 1 bisection -1<-2x < 1 so its -1/2<x<1/2

2) -1 < -x/2 < 1 bisection -1 < 1/3 x^2 < 1 so its -sqrt(3) < x < sqrt(3)

3) -1 < y/16 < 1 so its -16<y<16
Reply 3
the answers for the three questions are;

|x|<1/2

|x|<sqrt3

|y|<4

respectively

here are sum examples;

for (1+x)^-1 the set of values for x must be: |x|<1

for (1+2x)^-1 " " " : |x|<1/2

wot i dont understand is the questions that can be split up into partial fractions. Im guessing that u just take the denominator that requires the smallest value of x to be valid and then it applies to the whole function. so that sorts out 1 and 2 but 3 is still causing problems. Sorry i didnt actually number them - but in order - u no wot i mean
Reply 4
Ah sorry I misread the question.

I thought it asked where the functions were defined.
Reply 5
the book has |x|<4 for question 3. Thats wot i dont understand. Does the 16^1/2 that comes out when expanding have anything to do with it?
Reply 6
ryan750
the answers for the three questions are;

|y|<4



Are you sure you've typed this right? Is it perhaps instead

(16 + y^2)^(1/2)

which would be correct then.

As it stands Michael's answers are right.
Reply 7
ryan750
the book has |x|<4 for question 3. Thats wot i dont understand. Does the 16^1/2 that comes out when expanding have anything to do with it?


Is y = x^2 perhaps?
Reply 8
no it is only y. But i think that the book has a misprint for the answer because the keypoint summary says:

the expansion for (a + x)^n where n is a positve constant, is valid for |x|<a

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