(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

2 problems.

1)

Find an example of a function f such that :

the line y=2 is a horizontal asymptote of the curve y=f(x)

the curve intersects the line y=2 at the infinitive number of points

2)

The position of an object moving along x axis is given at time t by:

s(t)= 4t-4 if 2<t<8

and = -68 +t(20-t) if 8<=t<=10

Determine the acceleration and the velocity at any time t. Is the velocity continuous? Is acceleration continuous?

2. Relevant equations

3. The attempt at a solution

For the first one, I'm really puzzled how y=2 can be horizontal asymptote, AND that the curve intersects it at infinitive points.

I'm guessing that the function is y=2cos(1/x), as , y=2 is an asymptote even if my guess is right, how exactly should I solve that?

For the second one, I found derivatives of s and s'

s'= 4 if 2<t<8

s'= 20-2t if 8<=t<=10

s''=0 if 2<t<8 and

s"= -2 if 8<=t<=10

what then? how do i check if they are continuous?

I know the definition of continuous function and what exactly is horizontal asymptote, but I have no idea how to solve these two problems here :(.

Help!

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# Homework Help: Derivatives, continuity

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