Mathematics, 13.10.2019 23:20, omar2334

Ap calculus, me, i dont understand

Answers: 3

Show answers

Answers

answered: ashlyo

$\displaystyle y = Ce^\bigg{\frac{x^2}{2}} - 1$

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra I

FunctionsFunction NotationExponential Rule [Multiplying]: $\displaystyle b^m \cdot b^n = b^{m + n}$

Algebra II

Natural Logarithms ln and Euler's number e

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹

Slope Fields

Solving differentials Separation of Variables

Antiderivatives - Integrals

Integration Constant C

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

U-Substitution

Logarithmic Integration: $\displaystyle \int {\frac{1}{x}} \, dx = ln|x| + C$

Step-by-step explanation:

Step 1: Define

$\displaystyle y' = x(1 + y)$

Step 2: Redefine

Separation of Variables. Get differential equation to a form where we can integrate both sides.

[Division Property of Equality] Isolate x: $\displaystyle \frac{1}{1 + y}y' = x$ Rewrite derivative notation: $\displaystyle \frac{1}{1 + y} \ \frac{dy}{dx} = x$ Rewrite: $\displaystyle \frac{1}{1 + y} \ dy = x \ dx$

Step 3: Find General Solution Pt. 1

[Equality Property] Integrate both sides: $\displaystyle \int {\frac{1}{1 + y}} \, dy = \int {x} \, dx$ [Right Integral] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle \int {\frac{1}{1 + y}} \, dy = \frac{x^2}{2} + C$

Step 4: Find General Solution Pt. 2

Identify variables for u-substitution.

Set: $\displaystyle u = 1 + y$ Differentiate [Basic Power Rule]: $\displaystyle du = dy$

Step 5: Find General Solution Pt. 3

[Integral] U-Substitution: $\displaystyle \int {\frac{1}{u}} \, du = \frac{x^2}{2} + C$ [Integral] Integrate [Logarithmic Integration]: $\displaystyle ln|u| = \frac{x^2}{2} + C$ Back-Substitute: $\displaystyle ln|1 + y| = \frac{x^2}{2} + C$ [Equality Property] e both sides: $\displaystyle e^\bigg{ln|1 + y|} = e^\bigg{\frac{x^2}{2} + C}$ Simplify: $\displaystyle |1 + y| = e^\bigg{\frac{x^2}{2} + C}$ Rewrite: $\displaystyle |1 + y| = Ce^\bigg{\frac{x^2}{2}}$ Rewrite: $\displaystyle 1 + y = \pm Ce^\bigg{\frac{x^2}{2}}$ [Subtraction Property of Equality] Isolate y: $\displaystyle y = \pm Ce^\bigg{\frac{x^2}{2}} - 1$

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

Unit: Slope Fields

Book: College Calculus 10e

answered: Guest

answer: .75 km

step-by-step explanation:

answered: Guest

step-by-step explanation:

u take $30 minus $24. the answer/original($30)

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 15:00, DerikF9478

Saline iv fluid bags cost $64.20 for 24, 1000 ml bags from one supplier. another supplier sells 500 ml bags for $2 each. the hospital uses about 10,000, 1000 ml bags each month. nurses report that about half of the bags are more than half full when they are discarded. if you are going to use only one supplier, which would you choose and how much would you save with that choice? show calculator try it! if you buy 1000 ml bags, how many do you need to buy each month? type your answer in the space provided and click on the check answer button.

Answers: 3

continue

Mathematics, 21.06.2019 18:30, zovav1oszg9z

Analyze the graph of the cube root function shown on the right to determine the transformations of the parent function. then, determine the values of a, h, and k in the general equation.

Answers: 1

continue

Mathematics, 21.06.2019 21:00, cwebb4383

The sum of the first eight terms of an arithmetic progression is 9m + 14. the fifth term of the06 progression is 2m - 6, where m is a constant. given that the first term of the progression is 26,find the value of the common difference, d and thevalue of m.

Answers: 1

continue

Mathematics, 21.06.2019 23:30, jordynp2615

In the diagram, ab is tangent to c, ab = 4 inches, and ad = 2 inches. find the radius of the circle.

Answers: 2

continue

Do you know the correct answer?

Ap calculus, me, i dont understand
...