Introduction to Limits
Interactive practice questions
An injured frog is stuck at the bottom of a well that is $8$8 m deep. It tries to jump out, but each jump injures it further and so it can only jump half as far as its previous jump.
If the frog's first jump takes it $4$4 m up the well, how far will it be after the second jump?
How far will it be after the third jump?
Assuming the frog can continue to jump in this fashion forever, will it ever get out of the well?
Yes. It will get out after two more jumps, since it only needs to go another $1$1 metre.
No. It will continue to approach the top of the well, but never reach it.
Yes. If it can jump forever in the correct direction, then it will eventually get out of the well.
No. The frog will eventually stop moving up the well at all.
A small toy car, which can move forwards and backwards at the same rate, has been left on. It is inside a trash compactor in which the walls are moving towards each other at a rate of $2$2 cm/s. Each time the car hits a wall, it immediately starts going in the opposite direction.