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:
Dakota has 94 books, while Darius has 144.
Step-by-step explanation:
Given that Darius and Dakota are roommates, and together they have 238 books, if Darius has 50 more books than Dakota, to determine how many books does Dakota have the following calculation must be performed:
Dakota = X
Darius = X + 50
X + X + 50 = 238
2X + 50 = 238
2X = 238 - 50
X = 188/2
X = 94
Therefore, Dakota has 94 books, while Darius has 144.
Answer:
a total of 4,500
Step-by-step explanation:
Answer:
154.521
Step-by-step explanation:
Have a good day!
Answer: 71
Step-by-step explanation: fine the new value and Divided by the old value then multiplied by 100 then you get your answer
