The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y = C₁ + C₂ cos(x) + C₂ sin(x), (-00, 00); y""+y' = 0, y(π) = 0, y'(π) = 8, y"(n) = -1 y =

Q: (-3x)² +1 if x # 4 3x + 13 if x = 4 Calculate the following limits. Enter "DNE" if the limit does…

A:

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

A:

Q: Vf(1, 3) =

A:

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

A:

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: Solution ) we have option 3rd  y"+ 4y = 0 Auxilliary equation  m2 + 4 = 0 m2 = -4 m = √( -4 )  m =…

Q: Sketch the vector field F. (Select Update Graph to see your response plotted on the screen. Select…

A:

Q: -2y -2y (²²7) dx + e dy = 0 ex + x

A: Different ial eq is homogenous.

Q: a. S ya +1 b+y+cya+1 b. ft² cos 3t dt dy where a 0 and c = 1/(a + 1).

A:

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: This question can be solved using the concept of differential equation.

Q: What is the maximum value of the function h(x) = 10x =—= 22² x² on the interval 0≤x≤ 40 and for what…

A:

Q: Let f(x) 2x + 7 if x 1 9 if x = 1 Determine whether f(x) is continuous at x = 1. If f(x) is not…

A:

Q: Find the sum of the areas of the shaded rectangles under the graph. Round to two decimal places.…

A: topic- Area of shaded region Area of rectangle =Length*width

Q: yP = VI cos²x D2+1 }루 ST 21 2 cos2sc T + ₂a { 1+ COS20 D2 + 1 HOW DID HE GET THE VALUE INSIDE THE…

A:

Q: A population grows according to an exponential growth model, with Po = 40 and P₁ = 72 - Complete the…

A: topic- exponential function

Q: Consider the following function. f(x) = x¹/⁹ + 5 (a) Find the critical numbers of f. (Enter your…

A:

Q: Find three positive numbers whose sum is 114 and whose product is a maximum.

A: follow the procedure given below.

Q: Let f(x) 4x + 25 if x - 5 if x = -5 2 Select all statements below that you agree with. Note: You…

A:

Q: Consider the following. u = (-10, 0, 8) v = (5, -9, 0) Find u x v. Determine if u x v is orthogonal…

A:

Q: Evaluate the definite integral: f (x · cos(2x)) dx. Enter the exact decimal value. A graph of y = x…

A:

Q: 7. Determine the intersection, if any, of the planes with equations x +y-z + 12 =0 and 2x + 4y - 3z…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first first question.…

Q: Find the following integrals. Do not add any constants of integration, as the resulting functions…

A:

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

A:

Q: how long will it take for the money in an account that us compounded at 8% interest to quadruple

A:

Q: Find the inverse function (if it exists) of f(x) = ln (1-2x). If the function is not invertible,…

A: NOTE: Refresh your page if you can't see any equations. . to find an inverse function, interchange…

Q: integral

A:

Q: Find all values of x and y such that Px(x,y) = 0 and Py(x,y) = 0 simultaneously. P(x,y) = 5x²2 -…

A:

Q: 15) I What is the average rate of change of f(x) = from x = -2 tox = 4? x-s X+3 b 24 7 M C. d. 25 21…

A: We know that the expression for the average rate of change between the interval x2≤x≤x1 is: Average…

Q: Match the differential equations and the description/s that is/ are true to the differential…

A:

Q: F(x, y, z) = -k At (-2,-2, -2) the vector is At (-2,-2, 2) the vector is At (-2, 2, -2) the vector…

A: Given vector field F(x,y,z)=-k Here k is constant

Q: . Find the open interval(s) on which the function is increasing and decreasing.

A: Given :f(x)=9x3-11x

Q: You go to the doctor and he gives you 14 milligrams of radioactive dye. After 12 minutes, 6.5…

A:

Q: 10. 2ste tds +(s²e-t - t)dt = 0

A:

Q: What is the domain of the reciprocal function of f(x) = 5x+1? {x € R\x2} c. b. (x=Rxs-) a. d. {x =R…

A: We can answer the question as below.

Q: Show that the function f(x,y) = 8x²y subject to 3x - y = 9 does not have an absolute minimum or…

A:

Q: Solve the differential equation by variation of parameters. y" + y = csc(x) y(x) =

A: Given y''+y=csc(x) Complementary solution: We will solve this equation by variation of parameters…

Q: Write an equation for the function graphed below -7 -6 -5 -4 -3 -2 5+ 4- 3- 2 1 -2- -3 -4- -5+ 1 2 3…

A:

Q: Given that log a ( 2 ) = m and log a ( 3 ) = n , write exact expressions in terms of m and/or n for…

A: Write expression in terms of m and n for each of the following.

Q: Simplify to an expression involving a single trigonometric function with no fractions. cos(-x)…

A:

Q: The arc length of a given function is determined by √1+f'(2) dz Find the length of f(x)= (2/3)…

A:

Q: Find the area of the region bounded by the parabola y^2=x+3 and the line x - y = -1

A:

Q: Write an equation for the transformed logarithm shown below, that passes through (3,0) and -5-4-3-2…

A: The graph is given as , Find the equation for the graph.

Q: Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule. Compare these…

A:

Q: Replacement Time An outboard motor has an initial price of $2,160. A service contract costs $400 for…

A: Topic:- application of derivatives

Q: 1. Sketch the graph of r=1-cos in polar coordinates. [3 marks]

A:

Q: Use the Laws of logarithms to rewrite the expression 3 (212. √/y13 in a form with no logarithm of a…

A:

Q: Please solve part d)

A: To determine the points on the curve y=tan-1x, where the slope of the tangent line is the curve…

Q: Question 25 Use the slopes of tangents to determine whether the function f(x) = -6x² + 36x is…

A:

Q: Find the Inverse function of f over the given interval. Describe the relationship between the…

A:

Q: Find three positive numbers x, y, and z that satisfy the given conditions. The sum is 40 and P =…

A: Given that    Three positive numbers x,y and z                The sum of these numbers is 40.…

Q: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.