Binomial Theorem
Can someone help me out with this question please 
It's 16a and 16b and then 4a on the next sheet. I keep getting different answers, I don't understand how you can find the factorial of an n in a bracket for example (n+1)! or (n+3)! or n(n+1)! the questions are attached below. Many thanks in advance!
It's 16a and 16b and then 4a on the next sheet. I keep getting different answers, I don't understand how you can find the factorial of an n in a bracket for example (n+1)! or (n+3)! or n(n+1)! the questions are attached below. Many thanks in advance!Scroll to see replies
Here are the links to the questions
Original post by Hollymae764
Here are the links to the questions
Not sure the images are right, but for
Q11) Factorize the expression (complete the square) before rooting it. Your root attempt isn't correct.
Q10c) Whats the problem with sketching this? Sketch 1/x then translate.
(edited 4 years ago)
The graph moves right but how far right, and yeah thanks I attached the wrong question oops
Original post by Hollymae764
The graph moves right but how far right, and yeah thanks I attached the wrong question oops
It doesn't move horizontally.
I don't understand I thought that it was basically the same as y = f(x-b)?
But obviously (1/x - b)
Original post by Hollymae764
I don't understand I thought that it was basically the same as y = f(x-b)?
Just put a point in that is on y = 1/x and think how that point moves.
Alternatively, rearrange the equation slightly.
Oh ok right so the graph moves up but how much again and where are the asymptotes y would still be one right?
Original post by Hollymae764
Oh ok right so the graph moves up but how much again and where are the asymptotes y would still be one right?
Rearrange the equation slightly and/or consider what x gave the previous asymptotes and does the same thing happen here?
So y +b = 1/x so y is increasing by b, but still don't get how you would draw that.
And 0 = x made it the previous asymptote but does this not count anymore since you -b, meaning -b would be the asymptote?
And 0 = x made it the previous asymptote but does this not count anymore since you -b, meaning -b would be the asymptote?
Original post by Hollymae764
So y +b = 1/x so y is increasing by b, but still don't get how you would draw that.
And 0 = x made it the previous asymptote but does this not count anymore since you -b, meaning -b would be the asymptote?
And 0 = x made it the previous asymptote but does this not count anymore since you -b, meaning -b would be the asymptote?
Asymptotes at x = 0 (vertical) and x -> +/-inf (horizontal)? The latter two are probably the ones to consider.
Also, be careful about "increasing by b".
Ok I get the asymptotes at x=0 but i really don't understand the other one
And should it be y+b?
And should it be y+b?
Original post by Hollymae764
Ok I get the asymptotes at x=0 but i really don't understand the other one
And should it be y+b?
And should it be y+b?
What happens to a reciprocal when x->inf for
y = 1/x
y = 1/x - b
That confirms the vertical shift. Similarly for x->-inf
Edit. Tbh, if you're not sure, just stick a few values into both functions/graphs. It will soon become obvious.
Is this correct?
And i got r = x+3 for question 11
Ignore b=2 on the page
And i got r = x+3 for question 11
Ignore b=2 on the page
Original post by Hollymae764
Is this correct?
And i got r = x+3 for question 11
And i got r = x+3 for question 11
Did you put a point in as suggested? If so, which one?
Q11, yes, completing the square gives (x+3)^2 so ...
(edited 4 years ago)
Is my graph wrong?
I made b=2 and then tried different x values such as 2, 4, 6, 2000 and saw that they got really close to 2 but never quite touched it. And if 2 was equal to b then b i thought should be the asymptote.
I made b=2 and then tried different x values such as 2, 4, 6, 2000 and saw that they got really close to 2 but never quite touched it. And if 2 was equal to b then b i thought should be the asymptote.
Original post by Hollymae764
Is my graph wrong?
I made b=2 and then tried different x values such as 2, 4, 6, 2000 and saw that they got really close to 2 but never quite touched it. And if 2 was equal to b then b i thought should be the asymptote.
I made b=2 and then tried different x values such as 2, 4, 6, 2000 and saw that they got really close to 2 but never quite touched it. And if 2 was equal to b then b i thought should be the asymptote.
One last time, put some points in :-). For b=2, y does not tend to 2 (horizontal asymptote)
y = 1/(big) - 2
Its what you did at gcse and if you don't fully understand the rules, its something to fall back on.
(edited 4 years ago)
Just to pick your brain a little more, how do you do a factorial of n when its in a bracket? We haven't be taught this as the teacher went over just the basics of binomial expressions. This was the question:
(n-2)!+(n-1)!+n! is the same as (n-2)!n^2 for n which is greater/equal to 2
(n-2)!+(n-1)!+n! is the same as (n-2)!n^2 for n which is greater/equal to 2
Original post by Hollymae764
Just to pick your brain a little more, how do you do a factorial of n when its in a bracket? We haven't be taught this as the teacher went over just the basics of binomial expressions. This was the question:
(n-2)!+(n-1)!+n! is the same as (n-2)!n^2 for n which is greater/equal to 2
(n-2)!+(n-1)!+n! is the same as (n-2)!n^2 for n which is greater/equal to 2
(n-2)! just means a factorial starting at n-2 so
(n-2)! = (n-2)*(n-3)*...*2*1
No real reason why you should have been explicitly taught it, its just notation.
So to answer question, factorize the common (factorial) part out of the 3 expressions and simplify what's left. Its a couple of lines and looking at the answer, you can almost guess what the steps are.
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