10. Determine the convergence of the following series using the root test. If the root test is inclusive, state so and determine convergence with another test. Σ n=1 n+1, n+2'

Q: Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 O A. B. ey eLny OD.y O E. None…

A: To find the integrating factor.

Q: Given lim f(x) = -5 and lim g(x) = -12, evaluate lim [5f(x)-2g(x)]. X→ 11 X-11 X→ 11 O lim…

A: Given that: limx→11f(x)=-5, limx→11g(x)=-12

Q: d (h) Find sec (arctan (0~))] do

A: We need to find out the derivative.

Q: A B C D lim /(x) = 0 x+2+ lim f(x) = 2 x →-2+ lim /(x) = 0 x+2- lim f(x) = -3 x--2 -5-4-3-2-1 Y -3-…

A: Find limit of function

Q: Solve for the value of C in the equation: O A. 1 (2xy4ey + 2xy³ + y)dx + (x²y4eY - x²y² - 3x)dy = 0…

A:

Q: Find the slope of the line containing the points (3, - 2) and (1, 6).

A: Given data:- The given points of line is, 3, -2 and 1, 6

Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A: Here we can create the required polynomial function in the below steps.

Q: 1. Given the vectors a³ = (2, −1, 3), b` = PQ` where P(1, 1, 1) and Q(5, 1, −1) and c³ = i̇ + j³ +…

A:

Q: Let ƒ(x) = x/x - 2. Find a function y = g(x) so that (ƒ ∘ g)(x) = x.

A:

Q: Determine the solution of the differential equation: 3(x² + y²) dx + x(x² + 3y² +6y) dy = 0.

A: To determine the solution of the following differential equation. 3x2+y2 dx+xx2+3y2+6y dy=0

Q: Find the directional derivative of f at P in the direction of a. f(x, y) = 13 tan (²); P(-14,14);…

A: The given function is fx,y=13tan-1yx. To find the directional derivative, find the gradient of f.…

Q: Use synthetic division to determine if the given value for k is a zero of this polynomial. If not,…

A: By using synthetic division method the solution of given problem is as follow

Q: present

A:

Q: Evaluate using integration by parts or substitution. Check by differentiating. (2x²-7x) e7x dx √(2x²…

A:

Q: 3. Consider the initial value problem y′ +y=1-², y(0) = 30› where yo denotes some real constant. (a)…

A: To find the solution of given differential equation.

Q: Shown below is the graph of the flow rate f(t) of a pipe, in gallons per minute. Here, t= the number…

A:

Q: What is the standard form of this linear equation in one variable: (y + 1)dx + (4x − y)dy = 0? |…

A:

Q: Find the area of the shaded region. r² = sin(20) 4

A: See this solution in below.

Q: Use the disk method to find the volume of the solid obtained by rotating the region bounded by x = 1…

A:

Q: Evaluate the following integral. z+7 z(z²+9) dz

A:

Q: According to one model that takes into account air resistance, the acceleration a(t) in m/s" of a…

A: Here is the solution:

Q: Find the directional derivative of f at the point P in the direction of a. P(4,0); f(x, y) = 4x³y³;…

A:

Q: Which of the following is a non-homogeneous function? tan³y/x OxLnx-xLny O x³ − xy + y² (y² + v²)³/2…

A: homogenous function is f( tx,ty ) = t^n f(x,y) option a) f(x,y) = tan (3y/x) now,…

Q: Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1 A. 1/4 B. 1/2 C. 3/4 D.…

A:

Q: A car sharing service offers a membership plan with a $30 per month fee that includes 10 hours and…

A:

Q: 15. Evaluate each expression using the given table of values: -2 -1 1 f(x) 1 0 -2 1 2 g(x) -1 b.…

A: To use the table of values for finding the values of given function.

Q: (g) Differentiate g(x) = /1-². cos¹ (√) 3

A:

Q: p(x)=3x^3−x^2−8x−25 k=3 Use synthetic division to determine if the given value for k is a zero of…

A: The given polynomial is  P(x)=3x2-x2-8x-25  check whether k=3 is a root of the polynomial or not.

Q: sinx What is the integrating factor of (1+x) y + 2y = - 1+x

A: We have to find integrating factor for given differential equation.

Q: lim 0-0 cos 0 - 1 20²

A: SOLUTION-

Q: Which of the following equations is NOT a variable separable differential equation? OA 2xydx + (x² +…

A: NOTE: Refresh your page if you can't see any equations. . check the first DE now all x variables…

Q: Find the slope and equation of the tangent line to the graph off at the given point 17.) f(x) = ln…

A:

Q: For the function f(x) = 5x² 2x, evaluate and simplif f(x+h)-f(x) h 11

A: f(x)=5x2-2x hence f(x+h)=5x+h2-2x+hf(x+h)=5x2+5h2+10xh-2x-2h

Q: Find the particular solution of each of the following. (4+sine)y'=e*(6soc² e* - ycose); y(ln x) =…

A:

Q: You want to make an 80° angle by marking an arc on the perimeter of a 12-in.-diameter disk and…

A: Given data:- The given angle is, θ=80° The given diameter is, d=12 in So, the radius is, r=6 in.

Q: Draw the following intervals on the number line. 1. [ -1, 4] 2. (4, 3p) 3. [ -2, 12) 4. [1, 32] 5.…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: 8. Find the limit of f(x) = lim f(x)= 4- 818 (Type a simplified fraction.) lim f(x) = 8118 (Type a…

A:

Q: On a part-time job, you are asked to bring a cylindrical iron rod of density 7800 kg/m³, length 88.6…

A:

Q: Devise an exponential decay function that fits the given data, then answer the accompanying…

A: Here, the equation used is: P=P0ekt...(1) where P is the pressure of the atmosphere at t=0 and k is…

Q: Solve for the value of C in the equation: (2xy¹ey + 2xy³ + y)dx + (x²y4e¥ − x²y² – 3x)dy = 0 when…

A: The given equation is; (2xy4ey+2xy3+y)dx +( x2y4ey - x2y2-3x)dy=0 y(1)=1.

Q: 38. Critical Thinking How many students receive each grade? Each student receives a grade of A, B,…

A:

Q: Which of the equations below is a second order nonlinear differential equation? O A. ¹^²x²y — (1 —…

A: We have to find second order non linear differential equation from given options.

Q: State whether the equation is ordinary or partial, linear or non-linear, and give its order and…

A: See this solution in below.

Q: The function s(t) describes the motion of a particle along a line. s(t) = t3 − 10t2 + 32t − 230…

A:

Q: Evaluate the derivative of the following function. 1) 6x H(x)= (5x +

A:

Q: Graph the functions in Exercises .37. y = sqrt(x + 4)         38. y = sqrt(9 - x)

A: Given data:- 37. y=sqrt(x + 4) 38. y=sqrt(9-x)

Q: Sketch the region bounded by the curve x 2 = y and the line x = volume of the solid generated by…

A: solution:-the region bounded by y=x2-2 & x=y+2revolving around y=1

Q: Similarly, approaching along the y-axis yields a limit equal to 0. Since these two limits are the…

A: Given that a limit problem and we solve this problem by using general property of limit.   Here i…

Q: Solve the following equations. Leave answer in exact form. 1. e³x = 5 2.5e-7 = 8

A: Given, e3x=5Taking ln on both sideln(e3x)=ln(5)We know that ln(ab)=bln(a)3xln(e)=ln(5)We know that…

Q: Evaluate the following limit: lim O O O 6x²+17x-3 lim x→∞ 5x²+14x-3 6x²+17x-3 lim x→∞ 5x²+14x-3…

A: