Use separation of variables to solve the following differential equati problems: (a) (b) dz dt dy dt (c) 2y = = = 2y-4, tez dy Xx y(2) = 5

Q: Find the interest rate needed for an investment of $7,000 to triple in 6 years if interest is…

A:

Q: Find the general solution of the differential equation. Use C for the constant of integration. dr =…

A: Given differential equation, drdp=8sin(p)

Q: Let R and S in the figure above be defined as follows: R is the region in the first and second…

A: Given y=3-x2 y=2x

Q: Find the volume of the solid of revolution obtained by rotating the region bound by the following…

A:

Q: List the points in the xy-plane, if any, at which the function z = 7+ (x + 5)² + (y + 3)² is not…

A:

Q: Find the derivative of the function. 5 6 y = 4√x + 6x⁽ dy dx ||

A:

Q: 1. Let f = {(1, 2), (3, 4), (2, 6), (5, 9}. a) Find the domain of f: {1, 2, 3, 4, 5} O {2, 4, 6, 9}…

A:

Q: Frequently, we encounter a need for two (different) linear transformations to Transform a…

A:

Q: -10 foci Find the foci and asymptotes, asymptotes Find an equation for the hyperbola. -5 (x, y) =…

A: Now the equation of hyperbola is of the form:y2a2-x2b2=1Here a=6Therefore:y236-x2b2=1

Q: 75. ex √ex +1 - dx

A:

Q: Determine the interval on which the function in the graph below is decreasi -12 -10 -8 O a. [6, 10]…

A:

Q: sőso 2p √√4-x² x²√x² + y² dydx

A:

Q: 2) f(x,y)=3(y² + x²y)³

A:

Q: Find the solution of the initial value problem. dy = dx y(x) = = 6x² + 8x; y(3) = 15 6x²

A:

Q: Find the derivative. f(x) = x³. log4(x) Give your answer using the form below. XA(B + C logo(X)) A =…

A:

Q: Suppose that the function with the given graph is not f(x), but f'(x). Find the open intervals where…

A: Given  for decreasing interval f'(x) < 0

Q: Find the Jacobian of the transformation: x = 7.es+t y = 5.es-t Jacobian (in equation form) = Hint:…

A: Given :x=7es+ty=5es-t

Q: Use the product notation to rewrite the following expression. (22 − 4) · (32 − 4) · (42 − 4) = Π

A:

Q: Suppose that a large farm with a known reservoir of gas beneath the ground sells the gas rights to a…

A:

Q: Find the average value of f(x)=x^3 on the interval [2,6]. Answer:

A:

Q: A rocket is shot straight up into the air with an initial velocity of 192 ft/sec, and its height s…

A: st=-16t2+192t

Q: Multiply ◄ O x-2 x+4 x²-5x+6 x²+3x-4 O 1x-3 (x-2)(x+2) O (x-3) ² O 1 (x-3)(x-1) (x-3)2

A:

Q: Suppose X and Y are random variables with the given joint density function. ») - {0.10- 0.1e-(0.5x +…

A:

Q: Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the marginal…

A:

Q: find the derivative.

A: We need to find the derivative of f(x)=esin x

Q: 1. To rationalize the numerator of multiplied by? a) 8√x + 27 2. Determine lim a) 0 x+3 x--3x²-9 3x…

A: (1) To rationalize the numerator of 8x+273x, to determine the expression by which  the numerator and…

Q: Find the general solution of the differential equation. Use C for the constant of integration. 3 X…

A:

Q: Use the scratch paper to complete the table below and estimate the value of the limy→6²-4y-12 f(y)…

A:

Q: Use scratch paper to complete the table below, and guess the value of the limx→12²-144 f(x) x f(x) X…

A: Here  f(x)=x3-1728x2-144 To determine  limx→12f(x)=limx→12x3-1728x2-144

Q: Ice is forming on a pond at a rate given by k√t where y is the thickness of the ice in inches at…

A:

Q: Find the open intervals on which the function f(x) = x+6√5-x is increasing or decreasing.

A:

Q: The graph of f is shown below. Evaluate each integral by interpreting it in terms of areas. 3 2 1.…

A:

Q: Use the Fundamental Theorem to calculate the definite integral. Give an exact simplified answer. 1…

A: I=∫-1111+y2dy Here the fundamental theorem of Calculus:  ∫abf(x)dx=F(b)−F(a)

Q: Find the domain and range of the function graphed below. 3 2 Domain: Range: 7 -5 -4 -3 -2 -1 -1 -2 2…

A: Need to find domain and range of the function. Since domain is the set of yof x for which function…

Q: 2. Find the derivatives of the following functions. (a) f(x) = e sec x

A: We have to solve the derivative of the given function.

Q: Find dx dy dx 11 d²y dx² x = t² + 3, y = t² + 9t = and d²y dx² For which values of t is the curve…

A: x=t2+3 , y=t2+9t

Q: Evaluate the limit assuming that limx→4 f(x) = −5 and limx→4 g(x) = 3. (Use symbolic notation and…

A:

Q: Determine lim_g(x) for g as in the figure. x-0.5 1.5 y 0.5 lim_g(x) = x→0.5 y = g(x) -X (Give an…

A: Find the limit limx→0.5gx

Q: Find the integral. Use C for the constant of integration. [ (Inx) dx

A: given  y=lnx differentiate both side dy=1/x

Q: H For each of the labelled points on the graph, classify the corresponding point on the graph of y =…

A: Application of derivative

Q: Given xY^(harr ) and ZW^(harr ) intersect at point A. Which conjecture is always true about the…

A:

Q: Use Theorem 2.1.2 to find the slope of the tangent line of f-1 at x = -1. Given f(x) = -2 + 4x/x + 3…

A:

Q: Use the General Power Rule to find the derivative of the function. g'(x) = g(x) = √9-7x

A:

Q: Consider the function f(x) == on the interval [3, 11]. Find the average or mean slope of the…

A:

Q: 10) Find the relative maximum and minimum values for the function below give the following…

A: We need to find the relative maximum and minimum values of the given function.

Q: Han is making a line plot of the seedlings his class grew. This is what he has done so far. 0 XX XX…

A: Han has made the following line plot representing the seedlings that his class grew.

Q: The velocity (in feet/second) of a projectile t seconds after it is launched from a height of 10…

A:

Q: 1. Fill in the chart. f(x) ex ax In x f'(x) f(x) arctan r arcsin x f'(x)

A: We need to find the given derivatives:

Q: s²-4 (s² +9)². 2 데

A: L-1s2-4s2+92

Q: What is the average rate of change of f(x) from x₁ = -7 to x2 = -3? Please write your answer as an…

A: