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Introduction to Limits

Introduction to Limits. Does limits of function exist?. Description of limits. Limits come in all different shapes and sizes. Some functions have limits at all points, while others contain holes. Some functions may not have a limit at all. Basic Limit Structure. x ⟶ c.

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Introduction to Limits

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  1. Introduction to Limits • Does limits of function exist?

  2. Description of limits Limits come in all different shapesand sizes Some functions have limits at all points, while others contain holes Some functions may not have a limit at all

  3. Basic Limit Structure x ⟶ c The above limit is read as, “The limit of the function f (x) as x approaches c.” Basically, this means that as x approaches some constant, f (x) will eventually become something;

  4. lim 2x+3 x ⟶ 1 lim 2x+3 x ⟶ 0 lim 2x+3 x ⟶ -3/2 Examples Evaluate the following limits and tell whether the limit exist. =5, ∴ limit exists = 2(1)+3 = 2(0)+3 =3, ∴ limit exists = 2(-3/2)+3 =0, ∴ limit exists

  5. lim 2x+3 -3 = x ⟶ -3 0 x+3 When does the limit of a function not exist? ∴ limit does not exist

  6. Properties of limits Constant Scalar Multiple Sum or difference Product Quotient Power

  7. FISH Techniques for Evaluating LIMITS

  8. (6)-6 1 1 1 0 lim x-6 lim x-6 ∴ limit exists Factor (x+6) x ⟶ 6 x ⟶ 6 (6+6) 12 (36)-36 0 x2-36 (X-6)(x+6) Dividing Out Technique undefined

  9. lim x2-12x+36 lim x2-81 lim 5-x x ⟶ 5 x ⟶ 9 15-3x 9-x x ⟶ 1 x2-7x+6 Practice: =⅓ , ∴ limit exists =-18 , ∴ limit exists = -5/0 , ∴ limit DOES NOT exist

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