What graph can y = cos^2(x^2)/ x^2 have, for x > 0 ?
Right! Analysing the function "y" we can see that the graph should not exist below the "x" axis, since all the elements that form "y" as a function are positive, no matter what values "x" takes. Providing " x>0 " of course.Moreover, for "y=0", then "cos^2(x^2)/ x^2 = 0 ", hence "x^2= pi/2". For "x>0" the only value that satisfies our equation is " x = sqrt(pi/2)",which means the graph should look like ( can not attach a picture :( ).
DG
Related MAT University answers
All answers ▸I've been doing specimen MAT admission test - but I couldn't figure out the answer to the parts III, and IV of question 6 (https://www.maths.ox.ac.uk/system/files/attachments/speca.pdf). Is there some kind of a trick?
How do you differentiate ln(f(x))? Tricks like these occur commonly in STEP questions (including one I was looking at earlier today).
(Note this is the kind of exercise I would ask someone who is doing further maths and especially someone MAT/STEP) Sketch the graph of y=sin(1/x)
Deduce a formula (in terms of n) for the following sum: sum (2^i * i) where 1<=i<=n, n,i: natural numbers ( one can write this sum as: 1*2^1+ 2*2^2+ .. +n*2^n)