These are A level past papers, and unluckily I can't grab anything out of these. Any and all help is appreciated. I need a complete rundown on each question, this is for tomorrow. The more I can understand (mind you I'd rather understand then have you solve them for me without getting anything out of it), the better.
1: A curve has the equation
(i) Find the equations as the three asymptotes.
(ii) Find the coordinates of the turning points of the curve.
(iii) Draw a sketch of the curve and hence or otherwise, determine the set of values of y for which no point of the curve exists.
2: As described in this picture below...
3: The graph of
has the lines , and as asymptotes and a turning point at . Find the constants and and show that the graph has a second turning point.
Sketch the graph showing clearly its turning points and its behaviour as it approaches the asymptotes.
I'm at a loss in here, and I simply can't move deep enough to go to any clear solution. I get stuck and rather than showing my half scrubbed working I'd like to see how you'd do it from start to end with some thorough explanations. All 3 seem pretty similar, so working any one of them, whichever you find best, would be a big help.
Originally Posted by Lonehwolf
Hi, can someone help me sketch the curve y=x+cosx?
Also, I tried sketching the curve y = 2 (x)^1/2 + x and I'm thinking there's an asypmtote in it but I can't seem to prove that. Can someone also help me with this? please.(Worried)
( I'm supposed to show the intercepts , if any with the axes, any absolute or local extrema, the intervals over which f(x) is concave upward/downward, any points of inflection and the equations of any asypmtotes. )