Ask Singapore Homework?
Upload a photo of a Singapore homework and someone will email you the solution for free.
Question
junior college 1 | H2 Maths
One Answer Below
Anyone can contribute an answer, even non-tutors.
Hi! Can someone pls help me with this? I can’t get the answer, thank u so much!
Date Posted: 4 years ago
Views: 224
1/√(4 - x)
= (4 - x)-¹⁄²
= (4(1 - ¼x))-¹⁄²
= 4-¹⁄² (1 - ¼x)-¹/²
= ½ (1 + (-½)(-¼x) + (-½)(-½ - 1)/2! (-¼x)² +...)
= ½(1 + ⅛x + (-½)(-3/2)/2 (1/16 x²) + ...)
= ½ + 1/16 x + 1/256 x² + ...
(Maclaurin expansion)
So (1 + ax-¹) / √(4 - x)
= (1 + a/x) (½ + 1/16 x + 1/256 x² + ...)
Term independent of x
= 1(½) + (a/x) (1/16 x)
½ + a/16
½ + a/16 = 5
a/16 = 4½ = 9/2
a = 16 x 9/2 = 72
= (4 - x)-¹⁄²
= (4(1 - ¼x))-¹⁄²
= 4-¹⁄² (1 - ¼x)-¹/²
= ½ (1 + (-½)(-¼x) + (-½)(-½ - 1)/2! (-¼x)² +...)
= ½(1 + ⅛x + (-½)(-3/2)/2 (1/16 x²) + ...)
= ½ + 1/16 x + 1/256 x² + ...
(Maclaurin expansion)
So (1 + ax-¹) / √(4 - x)
= (1 + a/x) (½ + 1/16 x + 1/256 x² + ...)
Term independent of x
= 1(½) + (a/x) (1/16 x)
½ + a/16
½ + a/16 = 5
a/16 = 4½ = 9/2
a = 16 x 9/2 = 72
Edited.
" ½ + 1/16 x + 1/256 x² + ..."
Actually it's...
½ + 1/16 x + 3/256 x² + ...
Actually it's...
½ + 1/16 x + 3/256 x² + ...
Actually I already did extra and expanded up to there. It is sufficient to stop at the term in x for this question part
But no idea what that 1b) is (since she didn't show that part) so just did one extra term. The 1b) may have asked for up to a specific term
But no idea what that 1b) is (since she didn't show that part) so just did one extra term. The 1b) may have asked for up to a specific term
See 1 Answer
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
Good afternoon Sonia! Here are my workings for this question.
Date Posted:
4 years ago
No need to expand up to x³.
Oops, I expanded first because I not sure what question 1b actually asked for.
Usually they tend to ask three or four, and here they actually didn’t specify (even though we know only the first two terms are needed), so for the benefit of the doubt, I gave four terms.
Usually they tend to ask three or four, and here they actually didn’t specify (even though we know only the first two terms are needed), so for the benefit of the doubt, I gave four terms.
This question is similar to binomial expansion so not sure why she couldn't get the answer (unless expanded wrongly)
Sonia, it would be better if you provided the first part so as to set the context for the second part (that you are asking for)
Sonia, it would be better if you provided the first part so as to set the context for the second part (that you are asking for)
Well, it’s possible that the binomial skills learnt in A Maths has been partially forgotten already.
One of my students who have completed the full syllabus of A Maths two months ago actually forgot how to do logarithms learnt in Sec 3.
One of my students who have completed the full syllabus of A Maths two months ago actually forgot how to do logarithms learnt in Sec 3.
But this one is Maclaurin's series, a topic that is recently taught for JC1/Year 5. The expansion formulas are all in MF26 and would have been covered. Even if the student doesn't see the similarity to binomial theorem, applying the formula should be a piece of cake.
360 Tutoring Program