Approximate the area beneath y = sin x on the interval [o, π] using the Trapezoidal Rule with n = 4 trapezoids.

Q: The solution of the differential equation y' + 2xy = Ky when y(1)= K is

A:

Q: 1. f³₂ (x² − 3) dx -2

A: Given :∫-23x2-3dx

Q: Evaluate the following: fo(5x²y³ + 3x) dydx a. b. ff ex+ydA where R = {(x,y)|-x≤ y ≤x, 0≤x≤ 2}

A: To find the value of given double integrals.

Q: Evaluate the integral √ (k+ 2) ( k + 3) dx

A: Note:- according to the company policy we can attempt only one question so please upload the next…

Q: 2. (4x³ - 3x² + 2x) dx

A:

Q: p and q are complex numbers such that pl = 7√2 and p+ql = 12√//3. On what interval must g fall on? O…

A:

Q: 1. Find the Inverse Laplace Transforms of the following. 4 1) -1 S-3

A: The general formula we have that  Laplace transform of eat u(t) is 1/(s-a)

Q: 1. I. Evaluate each determinant. -5 -3 3 -4

A: Given,            -5-33-4

Q: B. Find the derivative 11. f(x) = 5x³ 12. f(x)=(x²-3) (2x-3) 13. f(x)=(2²+5)(4x-3) of each of the…

A:

Q: Use finite difference approximation to find the values of y(0.25), y(0.5), and y (0.75) for the…

A:

Q: Questions 1-4: The graph of a function y = f(x) on the interval [-3, ∞) is shown below. Use the…

A: Given.

Q: Determine the volume produced by the region bordered by 32 IT 15 "1 x² - 4x - 4y + 4 = 0 and y = 1…

A:

Q: Calculate the area contained between the curve y = cos x,-<x<, and the line y = 1/2. T 3 √3 Option 1…

A:

Q: A population grows according to the model, 1400 e 0.06t where A is the population t years after the…

A:

Q: 5. Evaluate lim x→2 x² - 16 X x-2

A:

Q: family

A: Please refer to the image below

Q: Find the linearization f(x) = √x, L(x) = L(x) of the function at a. a=4

A:

Q: A rectangular bird sanctuary is being created with one side along a straight riverbank. The…

A:

Q: You deposit $2000 in an account with 4% annual compound interest. Complete the following, assuming…

A:

Q: Let R be the region in the first quadrant bounded by x^2 +y^2 =4, y^2 = -x+4 and y=0. Set up the…

A:

Q: the Following differential equation ²²=1+ P²

A:

Q: 1. Find the area bounded by the curve y = x^2  and the x-axis and the ordinates x = 0 and x = 2 2.…

A:

Q: The given integral is equal to cos 3t dt 5 + 3 sin 3t O (1/3) In 15 + 3 sin 3t| + C O (1/9) In 15 +…

A: To find out the integration.

Q: The equation y-(5)=2(x-(3)) in slope intercept form is y=?

A: The equation y-(5)=2(x-(3)) in slope intercept form is y=?

Q: Given the definite integral, its limits are to be substituted to x³ dx x + 1 x² x² 2 x3 3 Option 1 +…

A: Given problem:-

Q: A cylindrical can without a lid is to be constructed to contain 800 ml of liquid. Determine the…

A: This question can be solved using the concept of maxima and minima.

Q: 1. Given the following vectors: u=(1, 2,-4) and v=(2, 3, 5) Find: a) u.v b) u.u c) (u.v) v d) angle…

A:

Q: limits

A: L'Hospital's rule apply only when there is 0/0 for ∞/∞ form.

Q: S dx -1 x-x² 2³√√x 1423 22 Option 1 Option 3 1425 22 Option 2 Option 4 1521 20 1523 20

A: Given: I=∫-8-1x-x22x3dx   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: C. Find the average rate of change of the given functions at the indicated interval. 1. f(x) = x² at…

A: We know that average value of function f(x) on given interval [a,b] is f(b)-f(a)b-a

Q: 6 F 0 28inx Cask ex

A:

Q: In spherical coordinates, the integral equivalent to None of these. 2πT π/2 2 S 6,²¹² 6² p² sin…

A:

Q: Find the derivative of the function and then evaluate at the given point. y = 2x² - 3x: (-1,5)

A:

Q: You deposit $2000 in an account with 3% annual compound interest. Complete the following, assuming…

A:

Q: 1. dx (x - 2)3 EXOX

A:

Q: (a) For a certain curve, y"=2. Find its equation given that it passes through P(2, 6) with slope 10.…

A: Note: according to the company policy we can attempt only one question so please upload the next…

Q: In the 2000 U.S. Census, a small city had a population of 45,000. By 2010, the population had…

A: Given  Population in 2000 = 45,000  Population in 2010 = 65148

Q: 1. Find the Inverse Laplace Transforms of the following. 3) 3s³+3s 56

A:

Q: Find the present value of a continuous stream of income over 5 years when the rate of income is…

A: On solving this we will get

Q: Solve for the slope of each of the given point of a function

A: Given that,

Q: Test for convergence / divergence. Find the limit if result is convergence.

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines

Q: Solve the differential equations i 4. y' + (tan x) y = cos²x, 8. e² y' + 2e² y = 2x

A:

Q: Classify the following ODE's with respect to order and linearity. a. 3x-y' - 5y = 7x³ - 8x+1

A:

Q: Find the area of the region bounded by the curves y = x² and y = -x² + 4x.

A: Here we have to find the area bounded by the curves.

Q: If the present value of an item is P and we experience an inflation rate of r for t years, what will…

A: solving the problem by finding the value of the future value.

Q: The rate of a continuous money flow starts at $600 and increases exponentially at 2% per year for 15…

A:

Q: (4) Let A be a nonempty subset of a bounded set B. Why does inf A and sup A exist? Show that (a) inf…

A: Let A be a not empty subset of a bounded set B.why does inf A and sup A exist? Show that a) inf…

Q: Use integration by parts to evaluate the integral. [2xe™x dx dx = [2xetx

A:

Q: я f (x) = (x2 + 3x)³ . (4x3 - 5x) 7 - -

A:

Q: Determine the x - y coordinates of the points where the parametric equation x = 5 sin²t y = 2 cost 0…

A: