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:
C
Step-by-step explanation:
Take the coefficient of the linear term and divide it by 2
9/2
Then square it 81/4
That should either be added to the 11 or subtracted from the 15.
The answer is C
Answer: C -7/3
Step-by-step explanation: Slope is rise over run, rise/run, and your line means your slope will be negative. So, you will first count straigt down from your firt point until you reach the line of the second point, which is 7. Next, you would count/run to the point, which is 3. Rise/run = -7/3. I hope this helps :)
Answer:
<u>-2</u>
Step-by-step explanation:
Find two points which lie on the line :
- Take (-2, -1) and (-1, -3)
Formula for slope (m) :
- m = y₂ - y₁ / x₂ - x₁
- m = -3 + 1 / -1 + 2
- m = -2/1
- m = <u>-2</u>
Answer:
-3
Step-by-step explanation:
5-2 is three
3 times -2 is -6
-9-(-6) is -3
(2,-3)
