Proceed to What I Know Chart for this part. 4) Activity 5: Check for Understanding (10 mins) ad of etnisianos A. Verify that the function y = e-3x is a solution to the differential etichets eteri d² y equation +-6y dx² eonie = 0.0

Q: -2-1 5 HA 4 у 3- 2 1 1 2 3 4 5 6 7 2 8 9 10 K

A:

Q: 4. y = x cos(In x) x²y" - xy + 2y = 0

A:

Q: 1. Find the volume of the solid that results when the shaded region is revolved about the indicated…

A:

Q: 1 4. f₁² (1-x²) dx 5 2

A:

Q: 2. y = ln x, y = 0, x = 0. Solve in two ways.

A:

Q: y(x tan x + In y) dx + tan x dy = 0.

A:

Q: Find the values of x, y and z that correspond to the critical point of the function 2 = f(x, y) =…

A: The given function fx,y=4x2+8x+7y+3y2 To find the critical points of the function

Q: x2-x1/3=0 x1/3(x5/3-1)=0 How do I get to the final simplification from the first equation?

A:

Q: 1. The graph of y=f(x) is given below. -4 2 2 -2 a) Find lim f(x) or state why it does not exist. 7…

A: Given

Q: A piece of cardboard measuring 8 inches by 10 inches is formed into an open-top box by cutting…

A:

Q: What is the form of the particular solutiony for the P differential equation y" - y = R(x) where…

A:

Q: 5. Find using first principles the slope of the tangent to f(x) = x² + 6x + 9 at x = -3.

A:

Q: (b) If z= 3x² + y² 4xy Hence, Show that find ôz dz dx dy Ox 3 3x a²z y a²z y ổr x ô and =0 8² z 2…

A:

Q: y (2x + y 2) dx O a. y (2x + y) = Ce - 2(x + y) dy = 0

A: y2x+y-2dx-2(x+y)dy=0 Lets check for exactness.…

Q: Consider the function f(x) = x² + 2x - 8 x - 3 a. Find the first derivative. f'(x) b. List any…

A:

Q: π 7. fz sin¹x cos¹ x dx

A: To evaluate the following integral by using Walli's formula.∫0π2 sin4 x cos4 x dx

Q: x²+1 lim x-5 √2x+2-2

A: We have to evaluate the limit.

Q: Consider the matrix A= Calculate a31 Calculate 932 755 826 5 2 6 e 9 dh n bf a

A:

Q: Evaluate the definite integral. 1. 2 cos-¹(x) √1-x² dx

A: Given Problem:- ∫-11-2cos-1x1-x2dx

Q: Please correct me if i'm wrong. The points where f(x) appears to concave downward appears to be…

A: Given , the point where f(x) appears to be concave downward appears to be (-2 , 2.9 )

Q: 7. Find: y = In dx √6x-5 [ Lex (x+1)³.

A:

Q: Find the radius of convergence, R, of the series. R = 00 I = n = 1 xn n45n Find the interval, I, of…

A:

Q: Answer: Use a triple integral to find the volume of the solid enclosed by the paraboloids y = x² +…

A:

Q: 10. (a) m = 0 L₂ (b) m = -² L₁ (c) m = 1 L3

A: Here, the given lines are with the slopes m=0m=-34m=1

Q: 12. Find the area bounded by the curve y = 3x(x - 2)² and the x axis.

A:

Q: Find the Indefinite Integral and check your result by differentiation. (Use C for the constant of…

A:

Q: so xe x dx

A:

Q: Consider the points A(3, 5, 1), B(7, -1, 0) and – C(-1, 3, 4). Find 2AB + BC. O(-1, 2, 3) O(0, -10,…

A: The given points are A3,-5,1, B7,-1,0 and C-1,-3,4

Q: 2. Given the vectors à = (a₁, a₂, a3) and b=(b₁,b₂, b3) show that a × b = -b xã.

A:

Q: 0 4 From a square piece of metal of side length 6 m, four squares are removed as shown in the…

A:

Q: f(x) = -2x² + 7 7x 10 - if x ≤ −1 if x > -1

A:

Q: Find the the e following: sinx first maclaurin four Series nonzero for terms of each (21) S² Tara d…

A:

Q: Problem Set question: The position function for a falling objects is given by s (t) = -16t² + vot +…

A:

Q: Evaluate the triple integral -3pi D x dV where E is the solid bounded by the paraboloid x = 6y² +…

A: Solution is given below:

Q: Find the the macl following:

A: Here, we need to find the Maclaurin series of tan-1x1+x2. Now,        Maclaurin series of function…

Q: Consider the revenue function R(x) and cost function C(x) for a company, given by…

A:

Q: Solve (y³ + 2y² +9y+18) dx = (5x²y² x²y + 17x²) dy

A: integration using partial fraction

Q: 1. The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in…

A:

Q: for evey 2 adults there are 3 children if 275 ppl attend how many kids are there

A: given that, for every 2 adults,there are 3 children total number of people=275 how many kids are…

Q: You are driving on a toll highway from King Road to Queen Road (a 50 km drive) in 25 minutes . Two…

A: Suppose, s(t) is the position function after t hours of time in km. Now, s(t) will be continuous and…

Q: Differentiate the following function. You do not need to simplify the derivative. h(x) = (lnx) ³…

A:

Q: 12- The system x' = x + 4y, y' = y + x has two eigenvectors.

A:

Q: dv/du = (uv)² — 2(u — v) — 2.

A:

Q: What is correct form of the particular solution associated with the differential equationy'''=8?

A:

Q: Find the Indefinite Integral and check your result by differentiation. (Use C for the constant of…

A:

Q: 2 (2y² + 5xy 4 Ο α. χ' (y² + 2xy = y + 2) = C O b. x4 (y² O 2y + 4) dx + x (2x + 2y − 1) dy = 0 - -…

A: The given differential equation is; 2(2y2+5xy-2y+4)dx+x(2x+2y-1)dy=0.

Q: Use any method to find the volume, V, of the solid obtained by rotating the region enclosed by the…

A:

Q: Test and k=/ each name K+ k³+1 of all the tests following. you for use. Conver

A:

Q: Suppose a company's profits are given by P = x^2 y, where x is the amount of money they spend on TV…

A: given  P = x^2 y x+y=12

Q: dv/du = (u — v)² — 2(u - v) - 2.

A: Here, the given DE is: dvdu=(u-v)2-2(u-v)-2...(1) Substitute u-v=p differentiating it with respect…