# 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)