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Limits. Definitions Precise Definition : We say lim f ( x ) = L if Limit at Infinity : We say lim f x = L if we. x a (. ) x ®¥. for every e > 0 there is a d > 0 such that can make f ( x ) as close to L as we want by whenever 0 < x - a < d then f ( x ) - L < e . taking x large enough and positive.
This theorem allows us to calculate limits by “squeezing” a function, with a limit at a point a that is unknown, between two functions having a common known limit at a. Figure 2.27 illustrates this idea.
The correct and most appropriate answer to a multiple-choice question will be, in each case, just one of the seven choices (A), (B), (C), (D), (E), (F), or (G). Answer all multiple-choice questions on the answer sheet, which is page 14 of this exam.
Based on Example 2.6, we make the following observation: It is possible for the limit of a function to exist at a point, and for the function to be defined at this point, but the limit of the function and the value of the function at the point may be different.
LIMITS BY STANDARD EXPANSIONS. Write down the first two non zero terms in the expansions of sin3x and cos2x . Hence find the exact value of. 3 x cos2 x − sin3 x . lim 3 . x → 0 3 x . sin3 x ≈ 3 x − 9 x 3 , cos2 x ≈ 1 − 2 x 2 , − 1. 2 2. Use standard expansions of functions to find the value of the following limit.
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 ...
Evaluate the limit: \Large {\lim_ {h\to -2}\frac {h^2+3h+2} {h+2}} Solution*. First, substituting the limit directly into the function, gives us: \Large {\lim_ {h\to -2}\frac {h^2+3h+2} {h+2} = \frac { (-2)^2 + 3 (-2) + 2} {-2 + 2} = \frac {0} {0}}
