Calculus question (1 Viewer)

[enigma_1]

I need some help with 3 e, the limit thing

thankss

 

[bottleofyarn]

Since 1/x -> 0 as x -> infinity, you can use this to describe what happens to y (and dy/dx) at the extremes of the graph. In this case you get y -> x and dy/dx -> 1 which means there's an asymptote. Then you can use all this to sketch the graph (including intercepts, asymptotes, stationary points found in previous parts).

 

[anomalousdecay]

Look at it this way. If x-->infinity, then y-->a number close to x.

This occurs as you know 1/x will tend to zero, but will not exactly be zero.

Also, y must tend towards x, because it is only a slightly larger number than x, since 1/x is NOT equal to zero, but very close to it.

So for d, you should get the two asymptotes as:

x --> infinity , y --> x and x --> negative infinity , y --> -x


for e)

You should note that x=0 is an asymptote.

You should note that the function is odd. This means that you only have to check half the points necessary in the question.

Make a rough scale (doesn't have to be accurate or linear, but must be logical)

Make dot marks of the asymtotes and label them.

Dot the stationary points and label them.

Sub in points between the asymptotes and the stationary points (which you may have done so in the previous sections) into your calculator and check the curve's shape.

Sketch the curve.