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3 years ago

Composition of functions

1 answer:

7 0

For example, in the composition of(f g)(x) = f(g(x)), we need to replace each x found in f(x), the outside function, with g(x), the inside function. Step 3: Simplify the answer. Examples – Now let's use the steps shown above to work through some examples. Example 1: If f(x) = –4x + 9 and g(x) = 2x – 7, find(f g)(x).

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A farmer wants to fence in a rectangular field that encloses 3600 square feet. One side of the field is along a river and does n

andriy [413]

Answer:

C(x) = $\$3.50(\frac{x^2+7200}{x})$

Step-by-step explanation:

Data provided in the question:

Area of the field = 3600 square feet

Fencing charges = $3.50 per foot

Let the side along the river be 'x' feet and the other side of the 'B'

now,

Area of rectangle = Bx = 3600 square feet

B = $\frac{3600}{x}$ feet

and total length to be fenced = x + 2B

therefore,

Total cost of fencing = Fencing charges × total length to be fenced

Total cost of fencing = $3.50 × ( x + 2B )

substituting the value of B from (1)

Total cost of fencing, C(x) = $\$3.50(x+2\times\frac{3600}{x})$

C(x) = $\$3.50(\frac{x^2+7200}{x})$

4 0

3 years ago

Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the co

jeka57 [31]

Answer:

<h2>A. The series CONVERGES</h2>

Step-by-step explanation:

If $\sum a_n$ is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

$\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho$

If $\rho$ < 1, the series converges absolutely

If $\rho > 1$ , the series diverges

If $\rho = 1$ , the test fails.

Given the series $\sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}$

To test for convergence or divergence using ratio test, we will use the condition above.

$a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}$

$\frac{a_n_+_1}{a_n} = \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\$

$\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\$

aₙ₊₁/aₙ =

$\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\$