To find a particular solution for the differential equation y" +9y=e with the variation of parameters method, we look for a particular solution of the form Yp u₁(x) sin 3x + u₂(x) cos 32- Select one: True False -

Q: Find the area of the shaded region. Enter your answer as a reduced fraction.

A: Area = ∫abupper curve -lower curvedxwhere a and b is the intersection points on x-axis.

Q: Which of the following statement is true for the alternating series below? 8 Σ(-1). n=0 n5+1 The…

A: Solution: Given data, ∑n=0∞(-1)n 1n5+1

Q: Convert to logarithmic form. - 4 2 N|O = 6,561 16

A: by logarithmic properties logxn=nlogxlogxx=1

Q: What is the definition of ? O [f'(x+h)-f'(x)]/h f" (x) lim h->0 [f(x+h)-f(x)]/h O [f(x+h)-f(x)]/h…

A:

Q: The difference between f'(3) and f'(x) is that f'(3) is a numerical value and f'(x) is a function of…

A: Given query is to find the statment is true or false.

Q: Use mathematical induction to prove the statement is true for every positive integer n. 20 + 40…

A:

Q: Use the graph to list f(x)dx, f(x)dx, and frosdx;ff'fox 10 fre f(x)dx in order from smallest to…

A: Use the graph to list ∫01f(x)dx, ∫02f(x)dx and ∫03f(x)dx

Q: f(x) = x4 - 8x³ +8 Answer the following by showing supporting work for each answer. Do not simply…

A: use the derivative property for finding the answer.

Q: Obtain the general solution. (EXACT EQUATIONS) 1. (3x²2y2) = 2xy dx

A: To obtain the general solution.3x2-2y2dydx=2xy

Q: Let f(x) = √5x² + 3x + 7 f'(x) = f'(2) =

A:

Q: Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index…

A:

Q: Find length of the cardioid r = 2(1 + cos 0)

A: Length of the cardioid, L=2∫0π r2+drdθ2dθ

Q: Consider the following table, and assume that f(x) and g(x) are differentiable functions with values…

A: Table of values are are given for fx and gx. We gave to find the value of h'3 where hx=1x+gxfx.

Q: mentary Problems nd the area bounded by the parabolas y = 6x-x² and y = x²-2 #/3 sq. units

A: Topic:- application of integration

Q: Suppose that tan0 COS tan Ꮎ = = 0 333 and 0 Find the exact values of cos and tan 2 π 元|2 <0<T. 02 .…

A:

Q: Use the graph of the function f to solve the inequality. (a) f(x) > 0 (b) f(x) ≤0 (a) The solution…

A: a) f(x)&gt;0: f(x)&gt;0 means the function lies above the x-axis. From x=-1 to x=2, the function is…

Q: A) Find the Laplace transform of the following function: f(t) = 0, 1 - t, G(s) = B) Find the inverse…

A:

Q: Given f(x) = 3x and g(x) = 9x2 + 1, find the following expressions. (a) (fog)(4) (b) (gof)(2) (c)…

A: Function

Q: Given 11 1(² f(x) dx = 3 and 10 f(x) dx = -3, find 10 f(x)dx.

A:

Q: f A/B dx where A = 2e^2x and B = e^2x +14e^x + 48 . Be sure to show all your steps clearly

A:

Q: Consider the function f(x): x²8x + 15 - x + 5 a. Find the first derivative. f'(x) b. List any…

A:

Q: Find the area of the shaded region. Enter your answer as a reduced fraction. 2 O 7 A = -1 squared…

A: Given equation of function that made the region are f(x)=x2-2 and g(x)=x

Q: Find the area of the region bounded by the graphs y=x+20 and y=x². yhapt

A: Given equations of curve y = x + 20 y = x2

Q: Determine the Wronskian of the following functions: f₁(x) = 1, f₂(x) = sinx, f(x) = cosx 0 1 O -1 O…

A:

Q: 11. Evaluate (4t³ + 5)dt

A: let  A=∫(4t3+5)dt∫tndt=tn+1n+1+c

Q: In numerically estimating 2 what value can be? O 3.000001 O 2.999999 lim f(x) O 3 x 3 X O 2.99999…

A: Given left hand side limit at x=3.

Q: se the given zero to find the remaining zeros of the function. f(x) = x³ - 7x² + 4x-28; zero: - 2i…

A: Topic:- application of algebra

Q: Let f(x)= 2-4 H-2 C 4x x 2 a) Does lim-2 f(x) exist? If yes, what is it? If not, explain. 321 b) Is…

A:

Q: provide

A:

Q: Given: z = x² + xy¹, x = uv² + w³, y = u + vew Find дz dv when u = 3, v = -2, w=0

A: Given that z=x2+xy4, x=uv2+w3, y=u+vew We have to find the value of ∂z∂v, when u=-3, v=-2, w=0.

Q: Question 3 A) Solve the given differential equation by variation of parameters: 2y" + y = 8x. B)…

A: (A) The differential equation is given as , 2y''+y'=8x Find the solution.

Q: ind / ( 2² +42 +5) de dx + C

A: To find ∫2x5+4x+5 dx.

Q: 1 For f(x) = 4x and g(x)= x, find (fog)(x) and (gof)(x). Then determine whether (fog)(x) = (gof)(x).

A:

Q: A company's revenue for selling x (thousand) items is given by R(x) = Find the value of x that…

A:

Q: 18 x² +9 (b) (gof)(2) (c) (fof) (1) (d) (gog)(0) Given f(x)= |x and g(x)= (a) (fog)(4) " find the…

A: Given,            fx=x and gx=18x2+9

Q: 13 Σ sin(k)= k=0 Question Help: Video

A: Topic:- trigonometry summation

Q: Evaluate the following integral using integration by parts. Ste A. -221 dt Use the integration by…

A: Let's solve given integration.

Q: Evaluate the definite integral. e² dr

A:

Q: Consider the following table, and assume that f(x) and g(x) are differentiable functions with values…

A:

Q: A function f(x) satisfies f(-7.3) = 6.6 and f'(-7.3) = -8.8. What is the equation of the tangent…

A:

Q: Use Cramer's rule to solve the system. 3x-2y4z = 39 2x-3y - 3z = 36 4x - 2y = 22 Write the fractions…

A:

Q: 5. A rectangle is constructed with its base on the diameter of a semicircle with, radius 1 cm and…

A:

Q: 8(k+1)-4 8(n+1)-4 4 8k-4 is term to both sides of the equation. 4+12+20++ (8k-4)= 4k² +20++ (8k-4)+…

A: Topic:- application of algebra

Q: Evaluate the integral. 9 13 cosh (√x) dx √√x

A: Given query is to find the integral.

Q: 6. Find f(x) for f(x)= 2X-7 3x-2

A:

Q: Evaluate the integral 49 S dx x(In x)5 11 49 dx S: 7 x(Inx)5

A:

Q: Approximate the area under the curve y = x² from x = 3 to x = 6 using a Right Endpoint approximation…

A: Given y = x2from x = 3 to x = 6 using right endpoint rule

Q: The acceleration of an object (in m/s²) is given by the function a(t) = 3 sin(t). The initial…

A:

Q: Use mathematical induction to prove the statement is true for every positive integer n. 20+40 +60++…

A:

Q: Obtain the general solution: (SEPARATION OF VARIABLES) 3. y' = y secx

A: