Topic 2 - Final

Question 1

2.3

What is a good idea to consider when you’re solving limits with functions that contain absolutes

Answer 1

Take the left and right hand side limit

Question 2

2.3

Solving squeeze theorem questions, what should you remember about establishing the range

Answer 2

Remember that if you are multiplying by another function you need to consider the range of that function. for example multipling by sin^2, the function cannot have the range -1 to 1 becuase suaring a value only has positive values, so it has to be 0 to 1 now

Question 3

What is a good function you can use to demonstrate that as the limit approches 0 the function approches infinity?

Answer 3

1/x^2

Question 4

True or false:

If a function is not differentiable at 0 then it is not continuous at 0

Answer 4

false

Other way around is true, but if it is not differentiable it may still be continuous, such as the absolute function

Question 5

Lets say you have a function and you have certain inputs and outputs of a ships time and altitude. Is the function invertible?

Answer 5

No becuase we know by the constraints of the question the function is continous, hence by the IVT if it has gone from 100km to 200km and then back down, it must have passed the same point at least once, so the function is not one to one