Quiz #2 Solutions

Tom Morley
Math1501
9/9/99

Problem 1

Part a)

Sx Sin[1/x] is caught between x and -x. By the Flyswatter principle,
the limit as x--> is 0.

Part b)

⁃Graphics⁃

The function blows up and occilates infinitely often. No limit.

Part c)

As x--> 0, the limits along irrations x and along rational x are the same,p namely zero
Limit is therefore zero.

Part d)

At x = &pgr; the limits are different

Problem 2

Left limit is 4, Right limit if 3

Problem 3

Part a)

Limit does not exist (Infinity is not a real number)

Part b)

Part c)

This can be seen as = ( Cos[x] -1)

Part d)