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ASHA 777 [7]
3 years ago
6

Use the power series representation of f(x)=

itle=" \frac{1}{1-5x} " alt=" \frac{1}{1-5x} " align="absmiddle" class="latex-formula"> to find a power series presentation of g(x)=\frac{15}{1-5x}
Mathematics
1 answer:
Sergeu [11.5K]3 years ago
4 0
For |5x|, we have

\dfrac1{1-5x}=\displaystyle\sum_{n\ge0}(5x)^n

and so

g(x)=\dfrac{15}{1-5x}=15\displaystyle\sum_{n\ge0}(5x)^n=3\sum_{n\ge0}5^{n+1}x^n

which is, again, only valid for |5x|.
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For the given function f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain.
kakasveta [241]

Answer:

a) (f + g)(x) = 9x + 1

Domain: x ε R

b) (f - g)(x) = (-5x + 13)

Domain: x ε R

c) (f.g)(x) = 14x² + 37x - 42

Domain: x ε R

d) (f/g)(x) = (2x + 7)/(7x -6)

Domain: (x ε R except x = 6/7)

e) (f + g)(7) = 64

f) (f - g)(2) = 3

g) (f.g)(3) = 195

h) (f/g)(x) = 1/3

Step-by-step explanation:

f(x) = 2x + 7, g(x) = 7x - 6

a) (f + g)(x) = f(x) + g(x) = (2x + 7) + (7x - 6)

(f + g)(x) = 9x + 1

Since x is defined for functions f & g for all real numbers, the domain of (f + g)(x) is x ε R

b) (f - g)(x) = f(x) - g(x) = (2x + 7) - (7x - 6)

(f - g)(x) = (-5x + 13)

Since x is defined for functions f & g for all real numbers, the domain of (f - g)(x) is x ε R

c) (f.g)(x) = f(x) × g(x) = (2x + 7)(7x - 6)

(f.g)(x) = 14x² - 12x + 49x - 42 = 14x² + 37x - 42

Since x is defined for functions f & g for all real numbers, the domain of (f.g)(x) is x ε R

d) (f/g)(x) = f(x)/g(x) = (2x + 7)/(7x -6)

x is defined for functions f & g for all real numbers, the domain of (f/g)(x) will be x ε R except when the denominator vanishes (that is, goes to zero). This will cause the function to take up values of ∞.

This will happen when 7x - 6 = 0, x = 6/7.

Therefore, the domain of (f/g)(x) is x ε R except the point, x = 6/7.

e) (f + g)(7) = 9(7) + 1 = 64

f) (f - g)(2) = -5(2) + 13 = 3

g) (f.g)(3) = 14(3²) + 37(3) - 42 = 195

h) (f/g)(27) = (2(27) + 7)/(7(27) - 6) = 61/183 = 1/3

Hope this Helps!!!

5 0
2 years ago
PLS HELP ME ASAP FOR 9) A and B (SHOW WORK!!) + LOTS OF POINTS!
statuscvo [17]
A.. 9.5*3.6=34.2 then 34.2/5.7= 6 so 6 is your answer

B. 16.2*5.7= 92.34 then 92.34/3.6= 25.65
4 0
3 years ago
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6. Fred is riding his bike in a race to earn money for a sick boy. Fred rides his bicycle at a top speed of 17 miles per hour. I
kogti [31]
17×4 is your answer.......
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3 years ago
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Can you guys solve 2 through 4? thanks, worth 40 points​
7nadin3 [17]
4- adding because it’s the opposite
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Ari is setting up a fish tank for his goldfish. The tank holds 15 gallons of water. If each gallon of water weighs 8.3 pounds, h
IrinaVladis [17]

Answer:

124.5

Step-by-step explanation:

All you need to do is multiply.

15*8.3=124.5

This is because The total water in Ari's fish tank has 15 gallons, and each gallon has 8.3, so you multiply.

6 0
2 years ago
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