Please don't just give me the answers (I can use my calculator for that), but explain how you get them by hand so I can understand them.
1) limit as Δx approaches zero OF (cos(π+Δx) + 1) / Δx
2) The function s(t) = -4.9t^2 + 200 gives the height in meters of an object that has fallen from a height of 200 meters. The velocity at time t = a seconds is given by: limit as t approaches a OF (s(a) - s(t)) / (a - t). At what velocity will the object impact the ground?
I just can't seem to make the algebra work on these two! Thanks for your help!
We know that:
So,
So, now you have:
From here you're going to need to multiply both sides of the fraction by , to get:
Now, the numerator looks pretty familiar and you can split the fractions:
From here you use the fact that we (should) know that:
Now, we have:
I believe you can solve it from here.
Yes, we haven't gotten to differentiation yet.
However, couldn't I stop at this step:
Because this limit is predefined as 0?
Anyway, thank you so much. I was looking at it this whole time not realizing I could simply solve the sin(pi) and cos(pi). I was treating them like variables too! It's amazing how you can overlook something so simple!