Let me express the equation clearly:
lim x→-9 (x²-81)/(x+9)
Initially, we solve this by substituting x=-9 to the equation.
((-9)²-81)/(-9+9) = 0/0
The term 0/0 is undefined. This means that the solution is not see on the number line because it is imaginary. Other undefined terms are N/0 (where N is any number), 0⁰, 0×∞, ∞-∞, 1^∞ and ∞/∞. One way to solve this is by applying L'Hopitals Rule. This can be done by differentiating the numerator and denominator of the fraction independently. Then, you can already substitute the x=-9.
(2x-0)/(1+0) = 2x = 2(-9) = -18
The other easy way is to substitute x=-8.999 to the original equation. Note that the term x→-9 means that x only approaches to -9. Thus, you substitute a number that is very close to -9. Substituting x=-8.999
((-8.999)²-81)/(-8.999+9) = -18
Answer:
C) 9.86%
Step-by-step explanation:
Given that:
Par value of the bond = $1000
Coupon rate = 5.25%
Years of maturity = 9
years to call = 3
price to call = 115% * 1000 = 1150
YTM of the bond = 0.0532
Using Excel formula:
The current price of the bond = P-V(0.0532/2, 9*2, 0.0525*1000/2, 1000)
= $995.04
The yield to call = 2 * RATE( 3*2, 0.0525*1000/2, 995.04, 1150)
The yield to calll = 9.86%
Answer:
y = -1x - 7
Step-by-step explanation:
y2 - y1 / x2 - x1
-6 - (-3) / -1 - (-4)
-3/3
= -1
y = -1x + b
-6 = -1(-1) + b
-6 = 1 + b
-7 = b
Answer:
1/18
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
Multiples of 3 between 1 - 9 = 3,6,9
Probability of picking a multiple of 9 = total multiples of 9 in the bag / total tiles in the bag
3/9
To transform to the simplest form. divide both the numerator and the denominator by 3
1/3
After picking the multiples of 3, the tiles are not replaced, tiles in the bag would now be 6
Probability of picking 5 = 1/6
1/6 x 1/3 = 1/18
