9. Determine by the root test if Ln=2 (4n-5\n 2n+1, converges or diverges.

Q: x² b. x²-4

A: Given: So,             f''(x)=x2x2-4''          =-8xx2-42'          =-8-3x2-4x2-43 Concave Up:…

Q: f(x) = In(1 + x5) %3D f(x) = Σ n = 1

A:

Q: dz Either show that the improper integral converges and find its value, or show that it diverges O…

A: To find if the given improper integral converges or diverges.

Q: Solve the initial value problem. dy + 9xy = 4x, y(0) = - 3 dx

A: This question is related to differential equations, we will solve it using given information.

Q: 0 4 0 4 0 0 zero matrix square matrix diagional matrix unit matrix O

A:

Q: dA when T = 5. dt dr Let A be the area of a circle with radius r. If dt 2, find %3D

A:

Q: Find the inverse of the function. f (x) = 14 – 5x³

A: Topic = Function

Q: da J 5—4г — 2:а? 5 – 4x 2.x 2

A:

Q: 8. 3. xp-

A:

Q: Express the Cartesian coordinates (-3,1) in polar coordinates in at least two different ways. Write…

A: We have to convert in polar coordinates.

Q: » / 13t – 41º + 4 dt = 6. (а) 1 - 5 Jū du: (b) dx = 4x3 (c)

A:

Q: 4) A is a set of m 2 1 positive integers. Show that exists a non-empty subset BCA such that the sum…

A: We are given that A is set of m positive integers where m≥1 . We have to show that there exists a…

Q: Match the graphs with the corresponding formulas. 1. Sn = 2 – 1/n 2. Sn = 2+1/n ? v 3. Sn = 2+…

A:

Q: Let y = 3x2. Find the change in y, Ay when x = 2 and Ar 0.2 Find the differential dy when x = 2 and…

A: We have to find solution

Q: Use logarithmic differentiation to find dy/dx. y = x8/x

A:

Q: V10 – Vx dx 3 2x2

A:

Q: ) Find of the implicit function a? + 5xy + y? – 2x + y – 6 = 0 at the point 1. . (1, 1).

A: Topic:- derivatives

Q: Draw an image o

A: answer is in next step

Q: A mountain climber is about to haul up a 70-m length of hanging rope. How much work will it take if…

A:

Q: 3. S sin³ 0 cos³ 0 d0

A: Given

Q: 5. Determine the horizontal asymptote. x³ +2x² -6 а. У- x? x* +3x° +x² –7 b. y: x* - 3x³ +8

A:

Q: | (6+xvF)dx

A:

Q: @ find dy 3\nx when 2)

A: As per guideline we have to solve one question Please repost other question again

Q: Find the greatest and the least values of the function y = x³ – 3x +3 on the 2 (a). interval [-, ).

A: Solve the following

Q: y" + 3y + 2y = x2

A:

Q: The solution of the differential equation below is dy Зу- + 4x = 0 dx

A: This is a problem of differential equation. Based on the general formula and concept of separation…

Q: Suppose that 5 J of work is needed to stretch a spring from its natural length of 32 cm to a length…

A:

Q: find dy/dx by implicit differentiation is 3y^2-xy=10

A:

Q: There is a function                                                           f(x,y)=3√x3 + y.…

A:

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

A:

Q: x3 dx J4- x4

A: ∫x3dx4-9x4Multiply & divide by -36 =-136∫-36x3dx4-9x4since, ∫f'(x)f(x)dx= 2f(x)

Q: Give 5 sample problems for Variable Separable (Differential Equation). Provide step by step solution…

A:

Q: 4. Find 2+1dt O V4x+1 O V16x? +1+v2 O 4/16x? +1 O V16x? +1

A:

Q: Find a cartesian equation for the curve r2 cos(20) = 4. Equation Use your answer above to identify…

A: Use the formula for conversion from polar to Cartesian coordinate.

Q: The sum 5 x) dx + -1, fx) dx can be written as a single integral in the form f(x) dx Determine a and…

A: Given query is to find the single integral fir the expression.

Q: Find the domain of the rational function. x-5 f (x) = x+8 Enter your answer in interval notation.

A:

Q: You will calculate L5 and U5 for the quadratic function y 2² + z + 14 between z = 0 and z = 2. Enter…

A: To solve the following problem

Q: Solve the initial value problem.

A:

Q: Find the general solution of the second-order differential equation: 4y" – 4y' + 13y = 0.

A: We have to find the solutions

Q: Fine the area of the surface obtained by the rotating the following curve about the x-axis. (The…

A:

Q: Se* tant e*dx

A: This question can be solved using the concept of indefinite integral.

Q: Evaluate the following limits for h(x) = { 1- 5z 120 (i) lim h(r) (ii) lim h(x) (ii) lim h(z)

A:

Q: Solve the equation .11 y" + 3y + 2y = x2

A: Solution is here

Q: An open box is to be made by cutting small squares from the corners of rectangular board and then…

A: let "x" be the length of the side of the square cut.Length= 8-2xWidth = 6-2xHeight =xVolume =…

Q: 9x2-42x+49 a. Simplify : 3x2-7x b. Solve the equations: i) 10 ii) 25x3 + 100x? – x – 4 = 0 ii) (х —…

A:

Q: 6 sin(x)dx

A:

Q: Set up an integral for the length of the curve. x = y2 + 6y, 0 s ys 6 OS Vay2. 37 dy OS Vay2+ 12y +…

A: We have to find out length

Q: dr J. (z+1)?

A:

Q: 1 Determine by the direct comparison test if Ln=1 2n+1 converges or diverges .

A: We have to find convergence test

Q: Dwing equations Is an exact different: v = 0 2xydx + (2 + an 1 O

A: We have to choose the correct option from the given options according to the given information