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Questions and Answers
Un population de bacterios cresce a un rata que es proportional al population presente. Si $P$ representa le population e $t$ representa le tempore, qual del sequente equationes differentional modella le situation?
Un population de bacterios cresce a un rata que es proportional al population presente. Si $P$ representa le population e $t$ representa le tempore, qual del sequente equationes differentional modella le situation?
- $\frac{dP}{dt} = k + P$
- $\frac{dP}{dt} = \frac{k}{P}$
- $\frac{dP}{dt} = kt$
- $\frac{dP}{dt} = kP$ (correct)
Qual del sequente functiones es un solution al equation differentional $\frac{dy}{dx} = 2x$?
Qual del sequente functiones es un solution al equation differentional $\frac{dy}{dx} = 2x$?
- $y = x^2 + 1$ (correct)
- $y = 2x + 5$
- $y = 2$
- $y = x^3$
Considerate le equation differentional $\frac{dy}{dx} = x - y$. Qual es le pendentia del campo de pendentias a puncto $(1, 2)$?
Considerate le equation differentional $\frac{dy}{dx} = x - y$. Qual es le pendentia del campo de pendentias a puncto $(1, 2)$?
- -1 (correct)
- 3
- 1
- 2
Si le campo de pendentias pro un equation differentional monstra que le solutiones se approximar a un certe valor de $y$ como $x$ cresce, que pote esser dicite de comportamento del solution a longe termino?
Si le campo de pendentias pro un equation differentional monstra que le solutiones se approximar a un certe valor de $y$ como $x$ cresce, que pote esser dicite de comportamento del solution a longe termino?
Que es le solution general al equation differentional $\frac{dy}{dx} = \frac{2x}{y}$?
Que es le solution general al equation differentional $\frac{dy}{dx} = \frac{2x}{y}$?
Flashcards
Qu'es un equation differential?
Qu'es un equation differential?
Un equation differential es un equation que involve un function incognite e su derivates.
Qu'es un equation differential de prime ordine?
Qu'es un equation differential de prime ordine?
Un equation differential de prime ordine involve le derivate prime del function incognite.
Qu'es le solution general de un equation differential?
Qu'es le solution general de un equation differential?
Le solution general de un equation differential es un expression que involve un constante arbitrar e satisface le equation pro omne valores del constante.
Qu'es un solution particular de un equation differential?
Qu'es un solution particular de un equation differential?
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Qu'es le methodo de separation de variabiles?
Qu'es le methodo de separation de variabiles?
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Study Notes
7.1 Modeling Situations with Differential Equations
- Differential equations model situations involving rates of change.
- Identify the quantities changing and their rates of change.
- Express the relationships between these quantities and their rates mathematically.
- Examples involve population growth, radioactive decay, and Newton's Law of Cooling.
7.2 Verifying Solutions for Differential Equations
- Verify if a given function satisfies a differential equation by substituting it into the equation.
- Ensure both sides of the equation become equal when the function and its derivatives are substituted.
- This process confirms whether a specific function is a solution to the given differential equation.
7.3 Sketching Slope Fields
- Slope fields visually represent the slopes of solutions to a differential equation at various points in a plane.
- Each line segment in the slope field corresponds to a specific slope at a particular point.
- Sketching slope fields helps visualize solution behavior.
7.4 Reasoning Using Slope Fields
- Slope fields illustrate how solutions to a differential equation behave.
- Analyze the direction of slopes and observe how solutions curve according to the slopes.
- Identify the behavior of solutions near different points using slope field diagrams.
- Analyze the effect of initial conditions on solution curves.
- Determine the general shape of solution curves without precise calculations.
- Identify where the solutions are increasing, decreasing, reaching maximum or minimum values, or exhibiting unusual behavior.
7.6 Finding General Solutions Using Separation of Variables
- Solve differential equations by separating variables.
- Isolate variables on opposite sides of the equation.
- Integrate both sides to obtain the general solution.
- Express the solution in terms of arbitrary constants.
7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables
- Determine particular solutions by applying initial conditions.
- Implement initial conditions to find numerical values for arbitrary constants in the general solution.
- This process results in a particular solution satisfying the given initial condition.
7.8 Exponential Models with Differential Equations
- Exponential models are solutions to differential equations.
- Population growth and decay, radioactive decay and compound interest are common scenarios.
- Model these and similar situations using differential equations.
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Description
Este quiz explora diferentes aspectos de equazioni differenti. Inclue modelage de situaciones, verificacion de soluciones e schizzamento de campi de pendenza. Preparar se para testar tu comprension de estos conceptos matematicos fundamentales.
