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  1. 201-103-RE - Calculus 1 WORKSHEET: LIMITS 1. Use the graph of the function f(x) to answer each question. Use 1, 1 or DNEwhere appropriate. (a) f(0) = (b) f(2) = (c) f(3) = (d) lim x!0 f(x) = (e) lim x!0 f(x) = (f) lim x!3+ f(x) = (g) lim x!3 f(x) = (h) lim x!1 f(x) = 2. Use the graph of the function f(x) to answer each question. Use 1, 1 or ...

  2. Evaluate this limit using the Limit Laws. Show each step. lim (1 + √3) (2 − 9 2 + 3) →. Solution: Using the Limit Laws, rewrite the limit. lim (1 + √3) (2 − 9 2 + 3) = [lim1 + lim√3] ∙ [lim2 − lim9 2 + lim 3] → →8 →8 →8 →8 →8. = [lim1 + 3 ] ∙ [lim2 − 9 (lim)2+ (lim)3] √lim. → →8 →8 →8 →8.

  3. AP Calculus ABWorksheet 7 Introduction to Limits There are no great limits to growth because there are no limits of human intelligence, imagination, and wonder. – Ronald Reagan Answer the following questions. 1 For the function f x x2 fx5, as the x-value gets closer and closer to 3, gets closer and closer to what value? 2

  4. Limits are a very powerful tool in mathematics and are used throughout calculus and beyond. The key idea is that a limit is what I like to call a \behavior operator". A limit will tell you the behavior of a function nearby a point.

  5. Limits and Derivatives Formulas. 1. Limits. Properties. if lim f ( x ) = l and lim g ( x ) = m , then. x → a x → a. lim [ f ( x ) ± g ( x ) ] = l ± m. x → a. lim [ f ( x ) ⋅ g ( x ) ] = l ⋅ m. → a. ( x ) l. lim = x → a. g ( x ) m. where m ≠ 0. lim c ⋅ f ( x ) = c ⋅ l. → a. 1. lim = where l ≠ 0. x → a f ( x ) l. Formulas. . n 1 lim 1 + = e.

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  7. In the overwhelming cases of real applications we only have to worry about limits when the function involves division by 0. For example f(x) = (x4+x2+1)=x needs to be investigated more carefully at x = 0. You see for example that for x = 1=1000, the function is slightly larger than 1000.

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