It is symbolized as x c lim fx L o It is read as Th e limit of fx as x

# It is symbolized as x c lim fx l o it is read as th e

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It is symbolized as: x c lim f(x) L o . It is read as: “Th e limit of f(x), as x approaches c, is L.” x It needs to be noted that the x-value in question (x = c), can be approached from either the left side, the right side or from both sides. Approaching x = c from the left side of x = c , x c lim f(x) ± o may yield a different LIMIT on the y value than if we were approaching x = c from the right side of x = c, x c lim f(x) ² o . ***** x c lim f(x) ± o and x c lim f(x) ² o are ONE-SIDED limits, ***** where as, x c lim f(x) o is the TWO-SIDED limit. If x c lim f(x) ± o = x c lim f(x) ² o = L , then x c lim f(x) o = L If x c lim f(x) o = L, then x c lim f(x) ± o = x c lim f(x) ² o = L NOTE : If the one sided limits are not equal , then the two-sided limit does not exist (DNE)!!!!
Below, you will find the graphs that we have previously completed. Use the graphs to find the requested limits. 1) f(x) x 2 ± 2) x ,x 0 f(x) undefined,x 0 ­ z ® ¯ 3) 2 x 9 f(x) x 3 ± ² a. ) f (2) = a) f (0) = a) f ( -3 ) = b) x 2 lim f(x) ± o = b) x 0 lim f(x) ± o = b) x 3 lim f(x) ± c) x 2 lim f(x) ² o c) x 0 lim f(x) ² o c) x 3 lim f(x) ² d) x 2 lim f(x) o d) x 0 lim f(x) o d) x 3 lim f(x) e) x 3 lim f(x) o e) x 2 lim f(x) o e) x 0 lim f(x) o 4) 2x 3, x 4 f(x) 5, x 4 ± t ­ ® ± ³ ¯ 5) 3x 2, x 2 f(x) 4, x 2 ± ² t ­ ® ± ³ ¯ 6) x f(x) x a) f (4) = a) f (2) = a) f ( 0 ) = b) x 4 lim f(x) ± o = b) x 2 lim f(x) ± o = b) f (2 ) = c) x 4 lim f(x) ² o c) x 2 lim f(x) ² o c) x 0 lim f(x) ± o d) x 4 lim f(x) o d) x 2 lim f(x) o d) x 0 lim f(x) ² o e) x 3 lim f(x) o e) x 0 lim f(x) o
Endpoints Left endpoint: Right endpoint: x 3 lim f(x) ± x 4 lim f(x) ± o x 3 lim f(x) ² x 4 lim f(x) ² o x 3 lim f(x) x 4 lim f(x) o Use your calculator to evaluate f(x) = 3 2 x x 7x 2 y x 2 ± ± ± ² for the given x-values that are approaching x = 2. Round to 4 decimal places. Use the table function on your graphing calculator. x 2.1 2.01 2.001 2.0001 2 1.9999 1.999 1.99 1.9 f(x) a) x 2 lim f(x) ± = c) x 2 lim f(x) = b) x 2 lim f(x) ² = d) f( 2) ±
M408 Calculus A Name Chapter 2 Worksheet 1 Fill in the following charts for the given functions. Use your calculator as needed. Then use your completed chart to estimate each limit. 1. f(x) = 2 x 4 x 2 ± ± x 0 1 1.9 1.99 2 2.01 2.1 3 f(x) lim x 2 f(x) ² o = lim x 2 f(x) ± o = lim x 2 f(x) o = 2. g(x) = 2,x 0 0,x 0 z ­ ® ¯ x ± 2 ± 1 0 1 2 3 g(x) lim x 0 g(x) ² o = lim x 0 g(x) ± o = lim x 0 g(x) o = 3. h(x) = x x x ± 3 ± 2 ± 1 0 1 2 3 h(x) lim x 0 h(x) ² o = lim x 0 h(x) ± o = lim x 0 h(x) o =
4. P(x) = 2 1 x x ± 2 ± 1 ± .5 ± .1 0 .1 .5 1 y lim x 0 P(x) ² o = lim x 0 P(x) ± o = lim x 0 P(x) o = 5. Q(x) = 11 x 11 x ² ± x ± .1 ± .01 ± .001 0 .001 .01 .1 Q(x) lim x 0 Q(x) ² o = lim x 0 Q(x) ± o = lim x 0 Q(x) o = Use the following graph to determine if the statements are true or false. 6. a) ³ ´ x 3 lim f x 3 ² _________ b) ³ ´ x 0 lim f x 0 ± o _________ c) ³ ´ x 0 lim f x 3 ± o _________ d) ³ ´ ³ ´ x 0 x 0 lim f x lim f x ± ² o o _________ e) ³ ´ x 0 limf x exists o _______ f) ³ ´ x 0 limf x 0 o _________ g) ³ ´ x 0 limf x 3 o _________ h) ³ ´ x 3 limf x 3 o _________ i) ³ ´ x 3 limf x 1 o _________ j) ³ ´ x 4 lim f x 1 ± o _________
Use the following graphs to determine the limits and the value of the function.

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• Fall '17
• Stephen Kurfess