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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. →∞ . . lim ( 1 + n )1. n = e.
Title: Calculus_Cheat_Sheet_All Author: ptdaw Created Date: 11/2/2022 7:20:00 AM
Evaluate f ( x ) at all points found in Step 1. minimum, or neither if f ¢¢ ( c ) = 0 . Evaluate f ( a ) and f ( b ) . Identify the abs. max. (largest function value) and the abs. min.(smallest function value) from the evaluations in Steps 2 & 3.
Limit Rules: Limit of a Constant: lim. →. Basic Limit: lim =. →. Squeeze Theorem: Let. = , and h be functions such that for all ∈ [ , (except possible at the limit point c), ( ) ≤ h( ) ≤ ( ). ] Also suppse that lim ( ) = lim ( ) = , then for any , ≤ ≤ , limh( ) =. → → →.
Calculus Cheat Sheet Limits. Limits. Definitions Precise Definition : We say lim = = → f ( x ) L if Limit at Infinity : We say lim f x L if we. x →∞. ( ) for every ε > 0 there is a δ > 0 such that can make f ( x ) as close to L as we want by whenever 0 < x − a < δ then f ( x ) − L < ε . taking x large enough and positive. .
7. Limits involving exponentials and logarithms86 8. Exponential growth and decay86 9. Exercises87 Chapter 7. The Integral91 1. Area under a Graph91 2. When fchanges its sign92 3. The Fundamental Theorem of Calculus93 4. Exercises94 5. The inde nite integral95 6. Properties of the Integral97 7. The de nite integral as a function of its ...
Find all critical points of f(x) in [a; b]. Evaluate f(x) at all points found in Step 1. Evaluate f(a) and f(b). Identify the absolute maximum (largest function value) and the absolute minimum (smallest function value) from the evaluations in Steps 2 & 3.
