 # Calculating Limits Using the Limit Laws

Yüklə 0,64 Mb.
 tarix 20.09.2018 ölçüsü 0,64 Mb. #70005  • ## In this section we use the following properties of limits, called the Limit Laws, to calculate limits. • ## Constant Multiple Law3. The limit of a constant times a function is the constant times the limit of the function. • ## For instance, if f (x) is close to L and g (x) is close to M, it is reasonable to conclude that f (x) + g (x) is close to L + M. • ## Use the Limit Laws and the graphs of f and g in Figure 1 to evaluate the following limits, if they exist. • ## Therefore we have • ## The left and right limits aren’t equal, so limx  1 [f (x)g (x)] does not exist. • ## The given limit does not exist because the denominator approaches 0 while the numerator approaches a nonzero number. • ## These limits are obvious from an intuitive point of view (state them in words or draw graphs of y = c and y = x). • ## More generally, we have the following law. • ## In general, we have the following useful fact. • ## When computing one-sided limits, we use the fact that the Limit Laws also hold for one-sided limits. ## Calculating Limits Using the Limit Laws • ## It says that if g (x) is squeezed between f (x) and h (x) near a, and if f and hhave the same limit L at a, then g is forced to have the same limit L at a. Yüklə 0,64 Mb.

Dostları ilə paylaş:

Verilənlər bazası müəlliflik hüququ ilə müdafiə olunur ©www.genderi.org 2023
rəhbərliyinə müraciət Ana səhifə