lecture1

# Lecture1 - 4 Constant Multiple Rule The limit of a constant times a function is the constant times the limit of the function 5 Quotient Rule The

This preview shows pages 1–7. Sign up to view the full content.

2.2 Limit of a Function and Limit Laws Limits of Function Values Example 1 How does the function f ( x ) = x 2 - 1 x - 1 behave near x = 1? 1

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

View Full Document
Let f ( x ) be deﬁned on an open interval about x 0 , except possibly at x 0 itself . If f ( x ) gets arbitrarily close to L (as close to L as we like) for all x suﬃciently close to x 0 , we say that which is read “the limit of f ( x ) as x approaches x 0 is L .” lim x x 0 x = lim x x 0 k = any constant k Example For the function f ( t ) graphed here, ﬁnd the following limits or explain, why they do not exist. a) lim t →- 2 f ( t ) b) lim t →- 1 f ( t ) c) lim t 0 f ( t ) 2
Example 4 Discuss the behavior of the following functions as x 0. a) U ( x ) = ± 0 , x < 0 1 , x 0 3

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

View Full Document
b) g ( x ) = ± 1 x , x 6 = 0 0 , x = 0 c) f ( x ) = ± 0 , x 0 sin 1 x , x > 0 4
The Limit Laws THEOREM 1 - Limit Laws If L,M,c and k are real numbers and lim x c f ( x ) = L and lim x c g ( x ) = M , then 1. Sum Rule: The limit of the sum of two functions is the sum of their limits. 2. Diﬀerence Rule: The limit of the diﬀerence of two functions is the diﬀerence of their limits. 3. Product Rule: The limit of a product of two functions is the product of their limits.

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: 4. Constant Multiple Rule: The limit of a constant times a function is the constant times the limit of the function. 5. Quotient Rule: The limit of a quotient of two functions is the quotient of their limits, provided the limit of the denominator is not zero. 6. Power Rule: The limit of a rational power of a function is that power of the limit of the function, provided the limit power is a real number. 5 Example 5 lim x → c x 4 + x 2-1 x 2 +5 = lim x →-2 √ 4 x 2-3 = THEOREM 2 - Limits of Polynomials If P ( x ) = a n x n + a n-1 x n-1 + ... + a , then THEOREM 3 - Limits of Rational Functions If P ( x ) and Q ( x ) are polynomials and Q ( c ) 6 = 0, then 6 Example lim x →-7 (2 x + 5) Example lim x → 5 4 x-7 Example 6 lim x →-1 x 3 +4 x 2-3 x 2 +5 = 7...
View Full Document

## This note was uploaded on 03/31/2008 for the course MATH 1205 taught by Professor Fbhinkelmann during the Spring '08 term at Virginia Tech.

### Page1 / 7

Lecture1 - 4 Constant Multiple Rule The limit of a constant times a function is the constant times the limit of the function 5 Quotient Rule The

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online