Let be
p(x)=<span>(x^{2} -1
q(x)=</span><span>3(x+1)
r(x)=1
the three coefficients of the equation
a is a singular point of the equation if lim p(x) =0
x------>a
so let's find a
</span> lim p(x) = lim x²-1=a²-1=0
x------>a x------>a
a²-1=0 implies a=+ or -1
so the sigular points are a= -1 or a=1
case 1
for a= -1
lim (x-(-1)) q(x)/p(x)=lim (x+1) 3(x+1)/x²-1=lim3(x+1)/x-1= 0/-2=0
x------> -1 x------> -1 x------> -1
lim (x-(-1))² r(x)/p(x)= lim(x+1)²/x²-1= 0/-2=0
x------> -1 x------> -1
lim (x-(-1)) q(x)/p(x) and lim (x-(-1))² r(x)/p(x) are finite so -1 is regular
x------> -1 x------> -1
singular point
case 2
a=1
lim (x-1)) q(x)/p(x)=lim (x-1) 3(x+1)/x²-1=lim3(x+1)/x+1= 3
x------> 1 x------> 1 x------> 1
lim (x-1))² r(x)/p(x)= lim(x-1)²/x²-1= =0
x------> 1 x------> 1
1 is also a regular singular point
Answer:
Step-by-step explanation:
Perpendicular lines have negative-reciprocal slopes.
The line contains point P(4, 8)
<u>Point slope form:</u>
<u>Given line:</u>
The slope of the perpendicular line is m = -1/4.
<u>The line in point-slope form is:</u>
Answer:
The first three statements are correct, the other two are wrong
Second to last problem: WRONG - Since the second to last problem is marked down by 40% we subtract 40% from 100% to get 60%. Now we just do 0.60*28 = 16.8 which makes the statement wrong.
Last problem: WRONG - The last one is marked down by 50% so that is 100% - 50% to get 50%. We do 0.50 * 28 to get 14, making the statement wrong.
The first 3 statements are correct, and the 2 last ones are wrong
- Hope this helped! :)
Brainiest is most appreciated:)
Answer: -23
Step-by-step explanation:
19 - 6(7) = y
19 - 42 = y
y = -23
Answer:
Charlie should use a stopwatch with minutes and seconds
Step-by-step explanation:
charlie should not count in his head as it is not accurate, he could count too fast or slow
Charlie should not look at that clock and the seconds will affect the 25 minutes, whether it be less or more
Charlie should not use an hourglass as he might flip it over too soon or quick and it's not very accurate
therefore using the stopwatch allows him to accurately and fairly keep track of the exact time