Question

Please help me with this question

http://s14.postimage.org/g9o26g127/Untitled.jpg

Answer 1

replace \(x\) by \(\frac{\pi}{2}\) in both expressions, set them equal, solve

Answer 2

i tried that but there is two unknowns

Answer 3

let see
since \(\sin(\frac{\pi}{2})=1\) first one is \(\frac{a}{2}\) and the second one is
\[\frac{k\frac{\pi}{2}+1}{\frac{\pi}{2}+1}\] meaning

Answer 4

oh i see right, but the question asks "what is the condition on \(a\) and \(k\) so we can write one in terms of the other, not actually find them.
let me do some algebra

Answer 5

hmm looks like we get
\[a(\pi+2)=2(\pi k+2)\] or
\[a=\frac{2(\pi k+2)}{\pi+2}\]

Answer 6

check my algebra
i suppose we could also solve for \(k\) in terms of \(a\) but you are right, you cannot find actual numbers, just the relation between them

Answer 7

however, part B is easy enough, assuming we have part A right.
for part B if \(g\) is to have a horizontal asymptote at
(y=2\) you know \(k=2\) so you can solve for \(a\) in that case. looks like it was good to solve for \(a\) in the beginning

Answer 8

i did the algebra again, got the same answer, so i think it is correct

Answer 9

Thanks, but im still confused to what you meant for part B. we plug in 2 for K ? and what are the conditions in part A. sorry but this question is confusing

Answer 10

lets answer the second question first

Answer 11

you are told
\[\lim_{x\to \infty}\frac{kx+1}{x+1}=2\] and since the degree of the top is the same as the degree of the bottom, this forces \(k=2\) so basically part B tells you \(k=2\)
so far so good?

Answer 12

yea i get it but its asking you for a value of (a) too not just K. or there isnt any?

Answer 13

yes, so now we return to the first question

Answer 14

we replace \(x\) by \(\frac{\pi}{2}\) in both expressions, and set them equal

Answer 15

you get
\[\frac{a}{2}=\frac{\frac{k\pi}{2}+1}{\frac{\pi}{2}+1}\]

Answer 16

i simplified the compound fraction on the right by multiplying top and bottom by 2 and got
\[\frac{a}{2}=\frac{k\pi+2}{\pi+2}\]

Answer 17

i get the algebra but what are the conditions? thats what i dont get

Answer 18

then i solved for \(a\) as \(a=\frac{2(\pi k+2)}{\pi+2}\) so that is the "condition"

Answer 19

"condition" in this case i take to mean "what is the relationship between \(a\) and \(k\)

Answer 20

in other words, solve for \(a\) in terms of \(k\)

Answer 21

oh i see sorry i was confused i thought they wanted a>0 or something like that.

Thanks so much!!

Answer 22

yw