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:
0.2297453
Step-by-step explanation:
Given that :
Total faces of = 12 labeled 1 - 12
Probability of showing a 2 ;
P = required outcome / Total possible outcomes
P(showing a 2) = 1 /12
Hence, probability of not showing a 2 ;
P(showing a 2)' = 1 - 1/2 = 11/12
Probability that atleast one of 3 cubes shows a 2 :
1 - P(none of the cubes shows a 2)
P(none of the cubes shows a 2) =
(11/12 * 11/12 * 11/12) = 0.7702546
1 - 0.7702546 = 0.2297453
Answer:
A.(AB/BC)=(CE/ED)
Step-by-step explanation:
Properties of Similar Triangles states two things
Corresponding angles are congruent (same measure)
Corresponding sides are all in the same proportion
That means AB/ BC = CE/ED
Answer:
The product of two negative integers is positive. (-a) *(-b) = ab True
The product of two integers with different signs is positive. (-a) (b) = -ab False
If two numbers are the same sign, then the product is positive.
a*b = ab -a * -b = ab True
The product of a positive and a negative is negative.
-a * b =- ab a * -b =- ab True
If the signs of two integers are different, then the product is positive.
-a * b =- ab a * -b =- ab False
Step-by-step explanation:
The correct answer is option D. The coordinates of the centre for the given equation of a circle is (5,4).
The complete question is as below:-
Which of the following points represents the centre of a circle whose
equation is (X - 5)2 + (y-4)2 = 25?
A. (-5,-4)
B. (5,-4)
C. (-5,4)
D. (5,4)
<h3>What is a circle?</h3>
The circle is defined as the locus of the point traces around a fixed point called the centre and is equidistant from the out trace.
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r the radius
(x - 5)² + (y - 4)² = 25 ← is in standard form
We can see that the centre of the circle is (5,4) by comparing the equation with the standard form.
Therefore the correct answer is option D. The coordinates of the centre for the given equation of a circle is (5,4).
Learn more about Circle here:
brainly.com/question/12908707
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