2n Let an = 3n +5 Determine whether {an} is convergent. Determine whether an is convergent.

Q: 2. Find an equation of the sphere satisfying the given conditions. a. It is concentric with the…

A: In this question, we want to find an equation of a sphere which is concentric with the given sphere.

Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

A:

Q: b/ Find the solution to the homogeneous differential equation below dy x²+y² dx 2xy

A:

Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

A:

Q: For the function glven below, use algebra to evaluate the limits lim f( メー→+ lim f(x), and limf(x)…

A:

Q: Given f(x, y) differential df = 10x?y then the total O 20xy dx + 10x² dy 20x dx + x2 O 2xy dx + x²…

A: For the solution follow the next step.

Q: Find the area bounded by y? = x3, y=2x

A:

Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

A: Topic = Integration

Q: the length of a child's square-based jewellery box is 5 cm more than its height. the box has the…

A: Topic  = Algebra

Q: Evaluate by using homogeneous D.E. 3 (3x? + y²) dx – 2xydy = 0 O ao3 = C(9x³ + y³) O ap3 = C(9x² +…

A: ANSWER: OPTION 2nd

Q: Solve through Bernoulli's Equation: * - y = xy O y-l +x – 1 = ce¯* O y + x – 1 = ce"

A: The standard form of Bernoulli's equation is: dydx+Py=Qyn Where; P & Q is the function of x.…

Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations hat are…

A:

Q: e length and breadth of the floor of a room are 30 ft. and 20 ft. pectively. Square tiles of 2 ft.…

A:

Q: 1. Determine whether the following integrals converge. (a) 1 dx x3

A:

Q: 11 2

A: We can solve this as follows:

Q: O 2y = x In cx?

A:

Q: Solve the following items and show your solutions. b.) Identify if the following functions are…

A: To determine whether the given function is homogeneous or not.

Q: For what value of the constant c is the function f continuous on (- o0, 0) where S (1)² – c if y 2

A:

Q: y = |x|, y = x² – 1, x = -1, x = 1 - г2 — 1,

A:

Q: Find the Laplace Transform of the following functions 2as 4) f(t)=tsinh(at) Ans. F(s)= (s² –a²} |

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Which of the following is not equivalent to sin 0?

A: We are asked to find which is not equivalent to sinθ

Q: The graph shown below is f(x) = 2x 2 - 1. If g(x) = Sốf(t)dt , find g '(3). %3D 4 2 X 54 3 -2 - V1 2…

A: g(x)=∫0xf(t)dtThenBy fundamental theorem of integral calculusg'(x)=ddx∫0xf(t)dt=f(x)g'(x)=2x2-1

Q: If the surface area of a cube is increased by 96%, by how much has the edge increased? 96% 92% O 40%…

A:

Q: 1- use Gauss Elimination to solve the following set of equations: 3x-y+z=-2 x+5y+2z=6 2x+3y+z=0

A:

Q: Consider the expression (3x² + 2/x)10 a) Find a simplified formula for the general term. (separate…

A:

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A: To determine the point of intersection of the given line and plane.

Q: f(b) – f(a) Find the value(s) of c that satisfy the equation = f'(c) in the conclusion of the mean…

A: We can find the value of c that satisfy the equation  f(b)-f(a)b-a = f'(c) .

Q: What are the relative extrema of the function f(x)=x^3+3x^2-24x+7 a. relative minimum of -4,…

A:

Q: Solve the following items and show your solutions. b.) Identify if the following functions are…

A: I am attaching image so that you understand each and every step.

Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 3, 4) (b)…

A: Given: xyz=12 (1,3,4)

Q: Learning Task 4: Given the equation x2 +y² =9. 1. Differentiate using implicit differentiation. 2.…

A: Since, the student has mentioned to solve only part numbers (4) and (5), so we are solving part…

Q: 1 dx V16 – x²

A:

Q: Solve the elementary applications of Differential equation: 1. Suppose that the quantity of a…

A: 1. Suppose that the quantity of a radioactive substance originally weighing Xo grams decomposes at a…

Q: Find the gradient of the function at the given point. w = x tan(y + z), (10, 5, -2) 2, Vw(10, 5, -2)…

A:

Q: What are the values of 8 between 0 and 2n (inclusive of 0 and 2t) that satisfy the trigonometric…

A: tan2θ-3secθ=-3⇒tan2θ-3secθ+3=0⇒2+sec2θ-3secθ=0⇒secθ=2, secθ=1⇒θ=π3+2πn, θ=5π3+2πn, θ=2πn

Q: II Three graphs labeled I, II, and III are shown above. They are the graphs of f,f', and f".Which…

A: Observe the each curve using slope and increasing decreasing properties.

Q: Solve the given initial-value problems. te dx +(y-1)dy=0; y(0) 0 4.43.

A: identify the differential equation and solve it.

Q: The barrel of a fountain-pen cylindrical in shape is 7 cm long and 5 mm in diameter. A full barrel…

A: Given that the fountain pen barrel is cylindrical in shape.

Q: Question Select your answer. A number is one more than thrice the other number. What is 1 the…

A:

Q: x = y² – y, x = y – y² |

A: The solution is given in the next step.

Q: 5. (xe*dx (1+x)2

A:

Q: What is/are the critical number(s) of the function S(2) = +4, f(z) :

A: f(x)=x2+4xDifferentiatef'(x)=x2x-x2-4x2f'(x)=2x2-x2-4x2f'(x)=x2-4x2

Q: If f(x, y) = xe2y + 6xy, then is dydx given by: e2y + 6 등 2e2y + 6 2 O None of these O 2xe2y + 6…

A:

Q: 2.Solve bernoulli (x ^ 2 + y ^ 2) * dx - xydy = 0

A:

Q: 4-x² 4. Evaluate [*, [* (r² + y°) dz dy dx. 4-. Hint: This iterated integral is a triple integral…

A: Cylindrical Coordinates:       Put x= r cosθ and y=r sinθ and z=zthen,      r = x2+y2 and θ =…

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: A detailed solution is given below

Q: g (x) .5 Compute g(1) + g' (1) + g" (1) + g" (1) + g'

A:

Q: 3. Scse*x dx

A: The objective of the question is evaluate the indefinite integral.

Q: Find the gradient of the function at the given point. w = x tan(y + z), (10, 5, -2) Vw(10, 5, -2) =

A:

Q: Find 4小1 机g:f el fof (メ= 区 x = 3x # S 3. f位)EX

A: We have to find the fog gof and fof functions.