MAT137 - Calculus with proofs Assignment #1 due on THURSDAY. TODAY: Limits geometrically WED: The definition of limit (Videos 2.5, 2.6)
Limits from a graph Find the value of 1. lim x → 2 f ( x ) 2. lim x → 0 f ( f ( x ))
Floor Given a real number x , we defined the floor of x , denoted by ⌊ x ⌋ , as the largest integer smaller than or equal to x . For example: ⌊ π ⌋ = 3 , ⌊ 7 ⌋ = 7 , ⌊− 0 . 5 ⌋ = − 1 . Sketch the graph of y = ⌊ x ⌋ . Then compute: 1. x → 0 + ⌊ x ⌋ lim 3. lim x → 0 ⌊ x ⌋ x → 0 ⌊ x 2 ⌋ 2. x → 0 − ⌊ x ⌋ lim 4. lim
More limits from a graph Find the value of 1. x → 0 + g ( x ) lim 2. x → 0 + ⌊ g ( x ) ⌋ lim 3. x → 0 + g ( ⌊ x ⌋ ) lim 4. x → 0 − g ( x ) lim 5. x → 0 − ⌊ g ( x ) ⌋ lim x → 0 − ⌊ g ( x ) 6. lim 2 ⌋ 7. x → 0 − g ( ⌊ x ⌋ ) lim
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