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

This preview shows page 11 - 17 out of 92 pages.

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)!!!!
Image of page 11
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
Image of page 12
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) ±
Image of page 13
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 =
Image of page 14
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 _________
Image of page 15
Use the following graphs to determine the limits and the value of the function.
Image of page 16
Image of page 17

You've reached the end of your free preview.

Want to read all 92 pages?

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture