Answer:
A) Particular solution:
B) Homogeneous solution:
C) The most general solution is
Step-by-step explanation:
Given non homogeneous ODE is
To find homogeneous solution:
To find particular solution:
Substituting 
in (1)
Equating the coefficients
The general solution is
from (2) ad (3)
The limit is x---->4-
The negative show that x approaches from the left
Now
As x approaches 4 from the left ... Means This number should be less than 4 (<4) but really close to 4.
Let's pick a Number
Say 3.99
Substitute this... You have
3.99/3.99-4
3.99/-0.01
If we choose x to be 3.999
we will have
3.999/-0.001
Notice the pattern... As x approaches 4 from the left... This limit will approach NEGATIVE INFINITY
Why?
As you approach 4 from the left... 3.9,3.99,3.999... You notice that the denominator becomes negative and EXTREMELY SMALL... and when you divide by an extremely small Number..... You'll get a relatively HUGE VALUE(You can try this... Use a calc... Divide any number of choice by a very small number... say.. 0.0000001.... You'll get a huge result
In our case... The denominator is negative... So it Will Approach a very Huge Negative Number
Hence
Answer.. X WILL APPROACH NEGATIVE INFINITY.
Vertical asymptotes are the zeroes of the denominator of a function
The denom. is x-4
Equate to zero to get the asymptote
x-4=0
x=4
Hence... There will be a vertical asymptote at x=4.
Have a great day!
Answer:
B. 30 ft
Step-by-step explanation:
The ladder is 32 ft long
The angle of elevation of the ladder is 70°
The height (h) of the top of the ladder to the ground is what we are to find.
= sin 70°
h = 32 × sin 70° = 30.07016387 or 30 ft (rounded off to nearest feet)
Answer:
40 miles away from home
To put it in yard would be 82,720
Step-by-step explanation:
Answer:
An ordinary annuity is a series of equal payments made at the end of consecutive periods over a fixed length of time. The opposite of an ordinary annuity is an annuity due, in which payments are made at the beginning of each period.
Step-by-step explanation:
