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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

For what values of p does the seriesconverge? For what values of p does it diverge? 00 k=1 1 kp
Find the general solution of the following differential equations. y' (t) + 3y = 0
Find the general solution of the following differential equations. y' (t) + 2y = 6
Find the general solution of the following differential equations. p'(x) = 4p + 8
Find the general solution of the following differential equations. y' (t) = 2ty
Use the Ratio Test to determine whether the following series converge.Data from in Ratio Test 00 k=1 k!
Find the general solution of the following differential equations. y'(t) =
Explain how the growth rate function determines the solution of a population model.
Use the Ratio Test to determine whether the following series converge.Data from in Ratio Test 8 00 2k | k=1k!
Find the general solution of the following equations. y'(x) = -y + 2
Use the Ratio Test to determine whether the following series converge.Data from in Ratio Test 00 k=1 2k kk
Find the general solution of the following differential equations. y'(x) = sin x 2y
Find the general solution of the following differential equations. y'(t) y +2 1² + 1
Find the general solution of the following equations. y'(x) + 2y = -4
What is a carrying capacity? Mathematically, how does it appear on the graph of a population function?
Use the Ratio Test to determine whether the following series converge.Data from in Ratio Test 8 k=1 k² 2 4k
Explain how the growth rate function can be decreasing while the population function is increasing.
Use the Ratio Test to determine whether the following series converge.Data from in Ratio Test 00 ke k k=1
Explain how a stirred tank reaction works.
Is the differential equation that describes a stirred tank reaction (as developed in this section) linear or nonlinear? What is its order?
Use the Divergence Test to determine whether the following series diverge or state that the test is inconclusive.Data from in Divergence Test k³ k=1k³ + 1
Describe the solution curves in a predator-prey model in the FH-plane.
Describe the behavior of the two populations in a predator-prey model as functions of time.
Find the general solution of the following equations. y'(x) = 2y + 6
Make a sketch of the population function (as a function of time) that results from the following growth rate functions. Assume the population at time t = 0 begins at some positive value. P'A 0 P
Find the general solution of the following differential equations. y' (t) = (2t + 1) (y² + 1)
Make a sketch of the population function (as a function of time) that results from the following growth rate functions. Assume the population at time t = 0 begins at some positive value. P' 0 P
Find the general solution of the following equations. u' (t) + 12u = 15
Find the general solution of the following differential equations. z' (t) tz 1² + 1 2 -
Make a sketch of the population function (as a function of time) that results from the following growth rate functions. Assume the population at time t = 0 begins at some positive value. P' 0 K P
Find the general solution of the following equations. v'(y) V --2/2 = 14
Make a sketch of the population function (as a function of time) that results from the following growth rate functions. Assume the population at time t = 0 begins at some positive value. P' K P
Find the solution of the following initial value problems. y' (t) = -3y + 9, y(0) = 4
Make a sketch of the population function (as a function of time) that results from the following growth rate functions. Assume the population at time t = 0 begins at some positive value. P'A P
Find the solution of the following initial value problems. Q'(t) = Q 8, Q(1) = 0
Make a sketch of the population function (as a function of time) that results from the following growth rate functions. Assume the population at time t = 0 begins at some positive value. ΡΑ Ο K P
Find the solution of the following initial value problems. X y'(x) = -— , y(2) = y = 4
Write a logistic equation with the following parameter values. Then solve the initial value problem and graph the solution. Let r be the natural growth rate, K the carrying capacity, and P0 the
Find the solution of the following initial value problems. u' (t) 1/3 (-)' , u(1) = 8
Write a logistic equation with the following parameter values. Then solve the initial value problem and graph the solution. Let r be the natural growth rate, K the carrying capacity, and P0 the
Find the solution of the following initial value problems. y'(x) = 4x csc y, y(0) TT/2
Use the method of Example 1 to find a logistic function that describes the following populations. Graph the population function.The population increases from 200 to 600 in the first year and
Find the solution of the following initial value problems. s' (t) 1 2s(t + 2)' s(-1) = 4, t≥ −1 5, 5 (-1)
Write the first four terms of the sequence {a}=1- n n=1.
Find the limit of the following sequences or determine that the limit does not exist. -1 tan n n
Find the limit of the following sequences or determine that the limit does not exist. {u/zu}
Evaluate the following geometric sums. 1 3 + 5 25 + 9 125 243 15,625
Find the equilibrium solution of the following equations, make a sketch of the direction field, for t ≥ 0, and determine whether the equilibrium solution is stable. The direction field needs to
Find the equilibrium solution of the following equations, make a sketch of the direction field, for t ≥ 0, and determine whether the equilibrium solution is stable. The direction field needs to
Use the method of Example 1 to find a logistic function that describes the following populations. Graph the population function.The population increases from 50 to 60 in the first month and
Find the solution of the following initial value problems. 0'(x) 4x cos² 0, 0(0) = π/4
Find the equilibrium solution of the following equations, make a sketch of the direction field, for t ≥ 0, and determine whether the equilibrium solution is stable. The direction field needs to
Find the equilibrium solutions of the following equations and determine whether each solution is stable or unstable. y' (t) = y(2-y)
Find the equilibrium solution of the following equations, make a sketch of the direction field, for t ≥ 0, and determine whether the equilibrium solution is stable. The direction field needs to
Find the equilibrium solution of the following equations, make a sketch of the direction field, for t ≥ 0, and determine whether the equilibrium solution is stable. The direction field needs to
For each of the following stirred tank reactions, carry out the following analysis.a. Write an initial value problem for the mass of the substance.b. Solve the initial value problem and graph the
Find the equilibrium solution of the following equations, make a sketch of the direction field, for t ≥ 0, and determine whether the equilibrium solution is stable. The direction field needs to
Find the equilibrium solutions of the following equations and determine whether each solution is stable or unstable. y'(t) = y(3 + y) (y – 5)
Find the equilibrium solutions of the following equations and determine whether each solution is stable or unstable. y' (t) = sin 2 y, for y < T
The following initial value problems model the payoff of a loan. In each case, solve the initial value problem, for t ≥ 0, graph the solution, and determine the first month in which the loan
The following initial value problems model the payoff of a loan. In each case, solve the initial value problem, for t ≥ 0, graph the solution, and determine the first month in which the loan
For each of the following stirred tank reactions, carry out the following analysis.a. Write an initial value problem for the mass of the substance.b. Solve the initial value problem and graph the
The following initial value problems model the payoff of a loan. In each case, solve the initial value problem, for t ≥ 0, graph the solution, and determine the first month in which the loan
Find the equilibrium solutions of the following equations and determine whether each solution is stable or unstable. y' (t) = y³y²– 2y
For each of the following stirred tank reactions, carry out the following analysis.a. Write an initial value problem for the mass of the substance.b. Solve the initial value problem and graph the
The following initial value problems model the payoff of a loan. In each case, solve the initial value problem, for t ≥ 0, graph the solution, and determine the first month in which the loan
For each of the following stirred tank reactions, carry out the following analysis.a. Write an initial value problem for the mass of the substance.b. Solve the initial value problem and graph the
The population of a rabbit community is governed by the initial value problema. Find the equilibrium solutions.b. Find the population, for all times t ≥ 0.c. What is the carrying capacity of the
A special class of first-order linear equations have the form a(t)y' (t) + a' (t)y(t) = f(t), where a and fare given functions of t. Notice that the left side of this equation can be written as the
A special class of first-order linear equations have the form a(t)y' (t) + a' (t)y(t) = f(t), where a and fare given functions of t. Notice that the left side of this equation can be written as the
A special class of first-order linear equations have the form a(t)y' (t) + a' (t)y(t) = f(t), where a and fare given functions of t. Notice that the left side of this equation can be written as the
Use separation of variables to show that the solution of the initial value problem is P(t) = P'(1) = rp(1 rP K K (P-1) ²₁. Po + 1 P K P(0) = Po
A special class of first-order linear equations have the form a(t)y' (t) + a' (t)y(t) = f(t), where a and fare given functions of t. Notice that the left side of this equation can be written as the
Consider the general first-order linear equation y'(t) + a(t)y(t) = f(t). This equation can be solved, in principle, by defining the integrating factor p(t) = exp(∫ a(t) dt). Here is how the
Consider the general first-order linear equation y'(t) + a(t)y(t) = f(t). This equation can be solved, in principle, by defining the integrating factor p(t) = exp(∫ a(t) dt). Here is how the
Consider a loan repayment plan described by the initial value problemwhere the amount borrowed is B(0) = + $40,000, the monthly payments are $600, and B(t) is the unpaid balance in the loan.a. Find
Suppose a battery with voltage V is connected in series to a capacitor (a charge storage device) with capacitance C and a resistor with resistance R. As the charge Q in the capacitor increases, the
Consider the general first-order linear equation y'(t) + a(t)y(t) = f(t). This equation can be solved, in principle, by defining the integrating factor p(t) = exp(∫ a(t) dt). Here is how the
Consider the general first-order linear equation y'(t) + a(t)y(t) = f(t). This equation can be solved, in principle, by defining the integrating factor p(t) = exp(∫ a(t) dt). Here is how the
Evaluate the following geometric sums. 8 100 k Σ3* k=0
Evaluate the following geometric sums. 10 k=0 K
A 100-L tank is filled with pure water when an inflow pipe is opened and a sugar solution with a concentration of 20 gm/L flows into the tank at a rate of 0.5 L/min. The solution is thoroughly mixed
Write the first four terms of the sequence {a}=1- n n=1.
Evaluate the following geometric sums. 20 k=0 Ult 2k
Write the first four terms of the sequence {a}=1- n n=1.
Find the limit of the following sequences or determine that the limit does not exist. 12 п 3n12 + 4 +4.
Write the first four terms of the sequence {a}=1- n n=1.
Evaluate the following geometric sums. All k=0 Alw k
Evaluate the following geometric sums. 12 15 Σ2* k=4
Write the first four terms of the sequence {a}=1- n n=1.
Find the limit of the following sequences or determine that the limit does not exist. 2e" + 1 en
Find the limit of the following sequences or determine that the limit does not exist. 3n³ - 1 2n³ + 1
Evaluate the following geometric sums. 5 Σ(-2.5)* k=1
Evaluate the following geometric sums. 6 k=0 71 k
Write the first four terms of the sequence {a}=1- n n=1.
Find the limit of the following sequences or determine that the limit does not exist. 3+1 + 3 3″
Write the first four terms of the sequence {a}=1- n n=1.
Write the first four terms of the sequence an = n + 1/n
Find the limit of the following sequences or determine that the limit does not exist. k {VOR 2 V9k² + 1
Evaluate the following geometric sums. 10 k=1 +1 k

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