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AlekseyPX
3 years ago
14

For a given input value bbb, the function ggg outputs a value aaa to satisfy the following equation. a-7=3(b+2)a−7=3(b+2)a, minu

s, 7, equals, 3, left parenthesis, b, plus, 2, right parenthesis Write a formula for g(b)g(b)g, left parenthesis, b, right parenthesis in terms of bbb.
Mathematics
1 answer:
Dvinal [7]3 years ago
8 0

Answer:

  g(b) = 3b +13

Step-by-step explanation:

The equation to be satisfied is apparently ...

  a−7=3(b+2)

Add 7 to both sides to get "a" as a function of "b".

  a = 3(b+2) +7

Now, we can simplify and write in the desired functional form:

  g(b) = 3b +6 +7 . . . . eliminate parentheses

  g(b) = 3b +13

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Help evaluating the indefinite integral
Dafna11 [192]

Answer:

\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }

General Formulas and Concepts:
<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:
\displaystyle (cu)' = cu'

Derivative Property [Addition/Subtraction]:
\displaystyle (u + v)' = u' + v'
Derivative Rule [Basic Power Rule]:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Integration

  • Integrals

Integration Rule [Reverse Power Rule]:
\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

Integration Property [Multiplied Constant]:
\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify given.</em>

<em />\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx

<u>Step 2: Integrate Pt. 1</u>

<em>Identify variables for u-substitution/u-solve</em>.

  1. Set <em>u</em>:
    \displaystyle u = 4 - x^2
  2. [<em>u</em>] Differentiate [Derivative Rules and Properties]:
    \displaystyle du = -2x \ dx
  3. [<em>du</em>] Rewrite [U-Solve]:
    \displaystyle dx = \frac{-1}{2x} \ du

<u>Step 3: Integrate Pt. 2</u>

  1. [Integral] Apply U-Solve:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du
  2. [Integrand] Simplify:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du
  3. [Integral] Rewrite [Integration Property - Multiplied Constant]:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du
  4. [Integral] Apply Integration Rule [Reverse Power Rule]:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C
  5. [<em>u</em>] Back-substitute:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }

∴ we have used u-solve (u-substitution) to <em>find</em> the indefinite integral.

---

Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27746485

---

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

5 0
2 years ago
Yaraliz has a bag of M&amp;Ms. She has 5 blue M&amp;Ms, 2 green M&amp;Ms, and 3
Dmitriy789 [7]
In the bag there’s is 5 blue and only 2 green she is most likely gonna pick blue. Who would even want to know that
5 0
3 years ago
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Hola alguien sabe y me explique como puedo resolver esto me dice que use los numeros dados y que haga una familia de hechos para
VMariaS [17]
5+4=9 es uno 4+5=9 es Otro 9-5=4 es Otro 9-4=5
6 0
3 years ago
Please help me out!!! :) 
Olin [163]

it would be > because the square root of 2 is more than 1.

8 0
3 years ago
Read 2 more answers
Use linear approximation to estimate f (2.85 )given that f (3 )equals 2 and f prime (3 )equals 5.
Allisa [31]

Answer:

Step-by-step explanation:

Given that,

f(3) = 2

f'(3) = 5.

We want to estimate f(2.85)

The linear approximation of "f" at "a" is one way of writing the equation of the tangent line at "a".

At x = a, y = f(a) and the slope of the tangent line is f'(a).

So, in point slope form, the tangent line has equation

y − f(a) = f'(a)(x − a)

The linearization solves for y by adding f(a) to both sides

f(x) = f(a) + f'(a)(x − a).

Given that,

f(3) = 2,

f'(3) = 5

a = 3, we want to find f(2.85)

x = 2.85

Therefore,

f(x) = f(a) + f'(a)(x − a)

f(2.85) = 2 + 5(2.85 - 3)

f(2.85) = 2 + 5×-0.15

f(2.85) = 2 - 0.75

f(2.85) = 1.25

5 0
3 years ago
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