integral test ∞ (α) Στ n n=1 8 b) 6) Σ n=1 -|~1/2 η2

Q: The graph above is a transformation of the function ² Write an equation for the function graphed…

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Evaluate the improper integral and state whether it converges or diverges. Show limit notation and…

A:

Q: Consider the curve r = (e³t cos(6t), e³t sin(6t), e³t). Compute the arclength function s(t): (with…

A:

Q: 2. If the portion of y 2 between x = 0 and x = 4 is rotated about the x-axis, what would be the…

A: Given that the region is bounded by the curve  between The surface area of the revolution about…

Q: The rational expression (x² − 2x+5)/(x² + x²) has partial fractions expansion Cx + D x² + 1 What is…

A:

Q: 10. () Give an equation of the tangent line to the graph of the function y = 3r²-2r-11 (it is the…

A: To give an equation of the tangent line to the graph of the function  at the point .

Q: Name all angles that are in standard position. y W X Y Z

A: If one ray of an angle is on the positive x-axis and its vertex is at the origin, the angle is said…

Q: Find the length of the curve. L = r (t) = 9ti + 12t j + 9t²k, 0 ≤ t ≤ 3

A:

Q: 21. Analyze the function below based on the following headings: domain, x & y intercepts, critical…

A:

Q: 2+ 4 y=x-2 f(x) -X

A:

Q: 12 Find the third Taylor polynomial for f(x) = X Select one: expanded about c = 1 a. P3(x) = 12-…

A:

Q: x² sin x (x, y) (0,0) x² + y² Determine whether lim exists.

A:

Q: Evaluate the integral I. I 1 = f (e¹i + 3t²j + ln (5t) k) dt i + j+ k + C

A: The given integral

Q: Given the equation y = 5 sin(3x + 18) + 2

A: we need to find out the horizontal shift.

Q: Determine if the sequences converge or diverge.  an = (ln n)/ln 2n   an = e^-n ln n   an = (3n…

A: • Sequence 1: Inconclusive • Sequence 2: Converges (e^-n dominates) • Sequence 3: Converges…

Q: 1. Apply the Divergence Test to the following series: 7 – 4n (2) Σ 2n + 4 n=1 (b) Σ n=1 303 +5 n2 –…

A:

Q: (2) n=1 n²-2√n +1 1-n-3n²

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the length of the curve F(t) = (eỗ cos (‡), eỗ sin(‡), eś) for 0 ≤ t ≤ 2. Arc length =

A: To find arc length of the curve

Q: lim (x, y)→(0, 0) sin (x² + y²) x² + y²

A:

Q: 2. Consider the sequence an given by 2n +1 n³ (a) Calculate the first four terms of the sequence (as…

A: The objective of the question is to analyze the sequence a_n = 2n + 1/n^3 for n ≥ 1. We need to…

Q: I'm practicing integration by parts and I want to make sure I am doing it correctly.  I have the…

A:

Q: Solve by using u-sub  Find integral  3X/X+4 DX

A: The given integral

Q: 1. Set up the integral to find the length of one cycle of the sine curve (y = sinx, where x is…

A:

Q: Apply the chain rule, in Leibniz notation, to determine dy dx at the indicated value of x. y = 4u(3…

A:

Q: ssume that functions f and g are differentiable with f(-4)= -2, f'(-4)= 4, g(-4)= -5, and g'(-4)=…

A:

Q: According to the video/notes, what would be the FIRST step in solving the matrix using row…

A:

Q: Find a first-degree polynomial function P₁ whose value and slope agree with the value and slope of…

A: The given function .The objective is to find the polynomial function  whose value and slope agree…

Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.) 5…

A:

Q: Find f'(a) if f(x)=√√√x-a+1. A B a+1 1 P C1 na D √√√a+1

A: we need to find out the derivative of the function at x=a.

Q: Determine the values of x for which the function (x) = sinx can be replaced the Taylor polynomial x³…

A: Given:function Taylor polynomial To find:values of x for which the function can be replaced by the…

Q: 1. Find the volume of revolution when the region bounded by f(x) = √2x + 1, y = 0, and x = 4 is…

A:

Q: - Find the area of a triangle PQR, where P = (1, - 2, 3), Q = (1, — 4, 1), an R = (1, 6, 0)

A: we need to find out the area of the triangle whose vertices are given.

Q: Let h(x) =tan(3x + 5). Then h' (4) is 3 sec² (17) 2 and h''(4) is

A:

Q: a. f²f² (x) dx 2 b. (f/²f(x)dx)²

A:

Q: y = x + 2 sin x (-л, π)

A: we need to find out the intervals where the given function is concave up and concave down.

Q: Completes parts A-C below: A. Find the marginal revenue function.      R(x)=x(150.09x)      R'(x) =…

A: Given thatA. we need to find the marginal revenue function.  B. We need to find the marginal revenue…

Q: Find the domain of the vector functions, r(t), listed below. using interval notation. a) r(t)…

A: To find the domain of the following vector functions.

Q: Find when 6x² + 2x³y - 2y² = 58. dy dx

A:

Q: Evaluate tr(g(t)) using the Chain Rule: r(t) = (et, et, -8), g(t) = 6t - 7 r(g(t)) = (

A:

Q: 3x √x +4 S dx (f) S 1 x(lnx)³ dx π/4 tan³ x cos³x (1) S™ dx

A:

Q: Instructions can be found in the image attached

A: (a).  f(x)=x100g(x)=(x+3)  (b).  f(x)=x1​g(x)=x3−1     Explanation:

Q: n=1 (2) Use the Limit Comparison Test to determine whether the series cot [ot n=1 All solutions need…

A:

Q: Solve the differential equation 3x²y"+ 20xy' - 6y = 0.

A:

Q: Evaluate the integral I. I = I = = [( (e¹i + 3t²j + ln (5t) k) dt i + j+ k + C

A:

Q: Test for convergence or divergence with the Direct Comparison Test.

A: See the answer given below Explanation:

Q: In Exercises 7-16, convert to rectangular form. 8. 2 sin 03 cc 7. r = 2 cos 0 9. r= tan 0 10. r = 4

A:

Q: 29. I must get from A to B across a rectangular manmade pond. The pond is 4 km in width, and 12 km…

A:

Q: velocity (feet/sec) 30 20 10 10 20 30 time (seconds)

A: The given figure

Q: 3. dy dt y 1+t +1²

A: We need to solve the differential equation.

Q: (x)b f(x) fi

A: The given figure