This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 0.1 0.99837 0.01 0.999980.01 0.99998 0.001 0.9999980.001 0.99999833 Definition of limit: Assume f(x) is defined for all x near c. but not necessarily at c. its e(t) we say the limit of f(x) as x approach c is equal to L. If f(x)4 becomes arbitrarily small when x is any number sufficiently close to c (not equal) We write: Lim f(x) =L We say f(x) converges to L as x >c Ex. Lim (x:>2) 2x+3 = 7 Absolute value of f(x) – L = absolute value of 2x+3 7 = absolute value of 2x4 = 2 times the absolute value of x2 Since absolute value of f(x) – L is a multiple of the absolute value of x2, Absolute value of f(x) – L become arbitrary small as x is close to 2. Theorem a) lim x>2 k=k b) lim x>c x= c ex. Lim x>0 e ^(1/x^2) = 0 x F(x) + 1 e ^1 +0.1 e ^100 +0.01 Example 1 (limit equals function value) F(x)= x Lim (x>4) x = 2...
View
Full
Document
 Fall '09
 JAY
 Math, Rate Of Change, Slope

Click to edit the document details