Solutions Homework 3

# Solutions Homework 3 - MATH 106 CALCULUS I FOR BIO. &...

This preview shows pages 1–3. Sign up to view the full content.

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.

Unformatted text preview: MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011 INSTRUCTOR: JOS ´ E MANUEL G ´ OMEZ Solutions Homework 3. (1) (10 Points) Determine if the following limits exist. When they do find their value (a) lim x → 2 e x +2 . (b) lim x → 3 + x 3- 27 x- 3 . (c) lim x → e x + 1 3 x + 1 . (d) lim x → 2 + 1 x- 2 . (e) lim x → √ x + 1- 1 x . Solution: (a) lim x → 2 e x +2 = e 2+2 = e 4 . (b) lim x → 3 + x 3- 27 x- 3 = lim x → 3 + ( x- 3)( x 2 + 3 x + 9) ( x- 3) = lim x → 3 + ( x 2 + 3 x + 9) = 3 2 + 3(3) + 9 = 27 . (c) lim x → e x + 1 3 x + 1 = e + 1 3(0) + 1 = 2 1 = 2 . (d) lim x → 2 + 1 x- 2 = + ∞ . (e) 1 2 INSTRUCTOR: JOS ´ E MANUEL G ´ OMEZ lim x → √ x + 1- 1 x = lim x → ( √ x + 1- 1)( √ x + 1 + 1) x ( √ x + 1 + 1) = lim x → (( x + 1)- 1) x ( √ x + 1 + 1) = lim x → x x ( √ x + 1 + 1) = lim x → 1 ( √ x + 1 + 1) = 1 2 . (2) (5 Points) Consider the function f ( x ) defined below f ( x ) = 1 x 2 if x > 1 , if x = 1 , x 3- x if x < 1...
View Full Document

## This note was uploaded on 01/20/2012 for the course CALC AS.110.106 taught by Professor Josegomez during the Fall '11 term at Johns Hopkins.

### Page1 / 3

Solutions Homework 3 - MATH 106 CALCULUS I FOR BIO. &...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online