review2f11

# review2f11 - 4 3 2 1 0.5 1.0 1.5 2.0

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

MAC 2311 Test Two Review, Fall 2011 Exam covers Lectures 10 { 18: Chapter 2, Section 10 { Chapter 3, Section 18 1. Evaluate each limit: a) lim x !¡1 ( x ¡ x 3 ) b) lim x ! 3 + arctan ± 4 x ¡ 3 c) lim x !¡1 p 9 x 2 ¡ 1 2 ¡ x d) lim x !1 ( e ¡ x sin x ) e) lim x ! 0 sin x ¡ x 2 x 2. Find each vertical and horizontal asymptote of the following functions: a) y = 4 x p x 2 + 1 ¡ 2 x b) f ( x ) = 2 e x 4 e x ¡ 3 3. Use the deﬂnition of derivative to ﬂnd a) d dx cos(2 x ), and b) d dx ± 4 p x . 4. Use the deﬂnition of derivative to ﬂnd f 0 ( x ) if f ( x ) = x 3 ¡ 2 x . Then ﬂnd the equation of the normal line to f ( x ) at x = 3. 5. If f ( x ) = ( 2 ¡ x j x j x < 0 2 + sin x x 0 , ﬂnd the following. For (a) and (b), use limits only. a) Is f ( x ) continuous at x = 0? b) Find f 0 (0) if possible. c) Find an expression for f 0 ( x ). d) Sketch the graph of f ( x ). 6. Let f ( x ) = ( xe tan x x x 6 = 0 0 x = 0 . Find f 0 (0) if possible. Is f continuous at x = 0? 7. Indicate whether each of the following statements is true or false.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

review2f11 - 4 3 2 1 0.5 1.0 1.5 2.0

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

View Full Document
Ask a homework question - tutors are online