{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

UFCalcSet8

# UFCalcSet8 - Exercises UF Calculus Set 8 1 Let f g h k be...

This preview shows pages 1–2. Sign up to view the full content.

Exercises UF Calculus Set 8 1. Let f , g , h , k be nonnegative functions with limits 0 , 1 , 1 , , respectively, as x a . What are the limits of the functions below as x a ? If it cannot be determined, write ”unknown”. (a) 4 f - 2 g (b) h - k (c) f g - h (d) h g + k (e) h · ( f + g ) (f) h · k f 2. Carefully justify the limits, step by step, from the limit laws. (a) lim x 2 x 2 - 1 x - 3 = - 3 (b) lim x 1 p x 2 + 3 x = 2 3. In each case, find a simple transformation of g ( x ) that is identical to f ( x ) for all points except those indicated. Use this fact to sketch the function f ( x ) . (a) f ( x ) = 2 x 2 + 5 x + 2 x 2 + 2 x ; g ( x ) = 1 x ; x = - 2 (b) f ( x ) = x - 1 x 1 - 1 x ; g ( x ) = x ; x = 0 , 1 (c) f ( x ) = ln x x 2 + x ; g ( x ) = ln x ; x = 0 4. Evaluate the limits: (a) lim x 0 x + 1 - 1 x (b) lim x 0 ( a + x ) 2 - a 2 x (c) lim x 3 ( x 2 - 9) 2 ( x - 3) 2 (d) lim x 0 - x p 1 + x - 2 (e) lim x 2 x 2 + 1 x - 3 x 2 - 4 (f) lim x 1 x 1+ x - 1 2 x - 1 5. Evaluate the limits using the squeeze principle. (a) lim x 0 x sin 1 x (b) lim x 0 sin 4 ( x ) x 2 , using the fact that sin( x ) x for all x 0

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
6. Evaluate the limits below involving absolute values: (a) lim x 1 + | x - 1 | x - 1 (b) lim x 1 - | x - 1 | x - 1 (c) lim x →- 3 x 2 + 3 x | x | - 3 (d) lim x 1 + x 2 + x - 2 | x - x 2 | (e) lim x 0 + 1 x + 1 | x | (f) lim x 0 - 1 x + 1 | x | 7. Evaluate the right, left, and overall limits at the points where
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

UFCalcSet8 - Exercises UF Calculus Set 8 1 Let f g h k be...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online