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# How can I sketch y=xsinx and y=(sinx)/x? watch

1. How can I sketch y=xsinx and y=(sinx)/x and what do they look like? I have no idea where to start so can someone help me please?

Thanks.
2. Find x-intercepts, y-intercepts, stationary points, asymptotes? Find a few points on it to get a general idea of what it looks like?
3. Why don't you try drawing a graph of sinx and then x (or 1/x) as an envelope and then multiply them together

You'll need to think about (sinx)/x at x = 0

(Original post by Rocious)
Find x-intercepts, y-intercepts, stationary points, asymptotes? Find a few points on it to get a general idea of what it looks like?
There are loads of stationary points (and they are shifted, not just the normal sin ones) and this just isn't a nice way of drawing these graphs
4. F(x) for x --> + infinity = 0
F(x) for x --> - infinity = 0
F(x) for x --> 0+ = 1 (Proof for this is too extensive for me to cover it at this time of night, however, it should be in your textbooks?)
F(x) for x --> 0- = 1

As x is close to infinity the absolute value of sin(infinity) is insignificant. However, the real value of sin(infinity) will change between -1 < x < 1. Hence, the function will 'go up and down' the x axis, going closer and closer to 0, for incredibly high or low values of x.

Edit: If you're in for more of a challenge, try sketching sin (1/x) for infinitesmal values of x!
5. for this graph: f(x)=sinx/x ... the y achsis interception is 1 ... because it tends to be 1 ... the graph moves then closer and closer to the x-achsis... !
6. O.o
how would you draw the curve y = A ? => y= A sin(x) ? how would you draw y = x or y = 1/x? ? => y= x sin(x) ? or y= (1/x) sin(x) ?

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