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Limmits

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• 1. The number Lis called the limit of the function f(x) as x approaches a, written
• 2. x x
• 3. x 0 x
• 4. lim h x 2 x 1 lim h x 1 x 1 lim h x does not exist x 1
• 5. ) If f(x) = c ( a constant function), then for any a x a n n ) where n is a positive x a integer
• 6. ) If f x and gx x a x a exist , then x a x a x a
• 7. ) If lim f ( x ) and g x x a x a exist , then x a x a x a
• 8. - If lim f ( x ) exists, then for any x a constant k, lim k f ( x )] k lim f ( x ) x a x a
• 9. lim f ( x ) gx x a x a f (x ) lim f ( x ) x a lim x a g (x ) lim g ( x ) x a
• 10. ) If lim f ( x ) exits, and n is a positive x a integer n n x a x a
• 11. If does not exist, since
• 12. ) 1 lim p 0 where p > 0 x x 1 lim p 0 where p > 0 x x
• 13. The limit does not exist
• 14. If f(x) is a rational function and is the term with greatest power in the numerator and is the term with greatest power in the denominator, then
• 15. A function f(x) is continuous at a point b if and only if: ) f(x) is defined at x = b ) lim f(x) exist x b ) ) lim f(x) = f(b) x b
• 16. Show that f(x) = / (x- ) is continuous at x= and discontinuous at x = f( )= / lim x f(x) = / =f( ) At x= the function is not defined.
• 17. The function is not defined at x=- So it is not continuous at x=- , but the limit exist.
• 18. A polynomial function is continuous at all points of its domain.
• 19. Find all points of discontinuity of f(x) = x - x + X + X- X + X - = (x+ ) (x- ). The denominator is zero when x=- or x= x=- Thus the function is discontinuous at x=- and x= only.