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e-lub [12.9K]
3 years ago
15

Find f(x) and g(x) so the function can be expressed as y= f(g(x))

Mathematics
1 answer:
noname [10]3 years ago
8 0
The answer would be 86
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Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your
Darina [25.2K]

Answer:

Given definite  integral as a limit of Riemann sums is:

\lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

Step-by-step explanation:

Given definite integral is:

\int\limits^7_4 {\frac{x}{2}+x^{3}} \, dx \\f(x)=\frac{x}{2}+x^{3}---(1)\\\Delta x=\frac{b-a}{n}\\\\\Delta x=\frac{7-4}{n}=\frac{3}{n}\\\\x_{i}=a+\Delta xi\\a= Lower Limit=4\\\implies x_{i}=4+\frac{3}{n}i---(2)\\\\then\\f(x_{i})=\frac{x_{i}}{2}+x_{i}^{3}

Substituting (2) in above

f(x_{i})=\frac{1}{2}(4+\frac{3}{n}i)+(4+\frac{3}{n}i)^{3}\\\\f(x_{i})=(2+\frac{3}{2n}i)+(64+\frac{27}{n^{3}}i^{3}+3(16)\frac{3}{n}i+3(4)\frac{9}{n^{2}}i^{2})\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{3}{2n}i+\frac{144}{n}i+66\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{291}{2n}i+66\\\\f(x_{i})=3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

Riemann sum is:

= \lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

4 0
3 years ago
Draw the solution for 4(2+10) when using the distributive<br> property.
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It would be 8 + 40 because you multiply the 4 by the 2 and 10
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3 years ago
High blood pressure is linked to what mineral? ​
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The high blood pressure is linked to sodium, postassium, calcium, and magnesium! Hope this helps! Brainleist would be appreciated
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2 years ago
The mean of 4 numbers is 15. 3 of the numbers are 18, 14 and 12. What is the other number?
Kisachek [45]

Answer:

Call the numbers a, b, c, d. What does it say if their mean is 15? That would be that added together then divided by 4 you get 15. So the number before you divided by 4, which is the sum, was 60. If you know some algebra, the equation (a+b+c+d)/4=15 gives the sum of 60 when you multiply both sides

4 0
3 years ago
Solve the equation: c + -22 = 16
elixir [45]

Answer:

c=38

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
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