-Free points- A 2-column table with 7 rows. Column 1 is labeled x with entries 2.9, 2.99, 2.999, 3, 3.001, 3.01, 3.1. Column 2 is labeled f (x) with entries 0.51160587, 0.50113874, 0.50011366, undefined, 0.49988639, 0.49886601, 0.48886948.
Use the table to determine a reasonable estimate for Limit of StartFraction 2 x squared minus x + 15 Over x cubed minus 5 x minus 12 EndFraction as x approaches 3?

One-half
One-fourth
3
DNE

*wink wink*

thx

Step-by-step explanation:

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.