It is estimated that x months from now, the population of a certain town will be changing at a rate of P'(x) = 3 + people per month. The current population is 100,000. Find P(x) and the level of population 27 months from now.

Q: Find dy/dx if y = log10(x² + 1)² D. dy/dx = log1o e (x² + A. dy/dx = 4x(x² + 1) 2x log10 e В. dy/dx…

A:

Q: Determine if the following integral converges or diverges. If the integral converges, find its…

A: To determine whether the given integral converges or diverges.

Q: A man 2 m tall is walking away from a lamppost which is 6 m tall at a rate of 2m/s. Find the rate of…

A:

Q: dy without first solving for y. dx e implicit differentiation to find ² + 3x + xy = 100 the given…

A: Topic:-  application of derivatives

Q: The volume of the solid obtained by rotating the region enclosed by y = 12, T = 2, I = 6, y = 0 |3|…

A:

Q: The limit lim (x c 1 X• COS is an indeterminate form of type 0· o. Select one: True O False

A: Given: limx→∞x·cos1x   As we know that; limx→afx·gx=limx→afx·limx→agx

Q: R is the region bounded by the lines y = x, y = -x, and x = 1. %3D

A:

Q: Solving Separable Equations: 1. dy - x-5 dx y2 2. = dx 3x²(1+ y?)

A:

Q: The rectangular coordinates of the point Pare (V3,-1, 2). In the cylindrical coordinates of P the…

A: Given

Q: Evaluate the integral: V1+ 7xd *Input answer as a decimal. Round-off to 2 decimal places.

A: Given query is to find the integration.

Q: Use the method of substitution to find the indefinite integral. Check your result by…

A:

Q: Use the method of substitution to find the indefinite integral. Check your result by…

A:

Q: divide f(x) and d(x), and write a summary statement in polynomial form and fraction form:…

A:

Q: "(x) If t(x) = Vx find ť'(x)" -2x O 2x -1/2x O 1/2x O None of these O o o o

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the integral: So V1+ 8xdx 3 *Input answer as a decimal. Round-off to 2 decimal places.

A: Given query is to find the value of the integral.

Q: 3. Solve equition system with Given function and using matrix representation: 3-x+ 3-y+ 4-z= 7 x -…

A: Given

Q: 11-30) Find the missing angles of the triangle below using the law of cosine. 18 V68 22 14

A:

Q: Evaluate dx -31 x a,

A:

Q: dy =Cos x Sinx cotX 8-

A: As we know that; The standard form of the linear differential equation; dydx+Py=Q Where P & Q is…

Q: On the circle x? + y² = r², find y". C. y": A. y" = =* E. None of these y -x3 -x2 - y? D. y" = В. у"…

A:

Q: 7.2Find the macrorin series of f(x)=(1+x)^(1/3) , by reacthe term n=4

A: Follow the procedure given below.

Q: 135 2. y = x³, y = x + 6, and 2y + 2 = 0 (Answer: s. u.) 4

A:

Q: 1 erivative of x²+2

A:

Q: 11. If m = 13 + 2\/42 a. Find the value of ym b. Find the value of m 1 c. Show that, m²Vm + 12987 m²…

A: A detailed solution is given below.

Q: y - 4y+ 4y = 2t2 + 4te2t + t sin2t

A:

Q: Evaluate the integral x³ - 3– 2x2 - 4 dx x3 -2x2

A: We have to find integration in this question.

Q: Evaluate the integral: V3 S arctan () da *Input answer as decimal round-off to 2 decimal places.

A: Given :∫13arctan1xdx

Q: Activity 1. Determine the antiderivatives of the following functions. 1. f(1) = (1+1)100 2. f(x) =…

A:

Q: find dy for ee Sin (メ+34) dx

A:

Q: he velocity vector? Di+O i+O k

A: Topic:- application of derivatives

Q: 1 dA; R = {(x, y) : r² + y² s 4, r 2 0, y 2 0}. /16- r2 – y?

A: Using polar coordinates, integration is evaluated.

Q: LogaX

A:

Q: Find the tangent line to the curve y = x + 2x3-2x2 -3x + 3 which is perpendicular to the line x- 3y…

A: Given :y=x4+2x3-2x2-3x+3Line : x-3y=2

Q: x/2 dy 2. - ५ = sin x dy +34 d x 2- X 2

A:

Q: Find Mx for the area bounded by y^2=4x and x^2=4y.

A: Given problem:- Find Mx for the area bounded by y2 =4x and x2 =4y.

Q: of the indicated portion of the curve. K.

A:

Q: dA; R= {(r,y): 0srs1,1 sys 4}.- %3D IR

A: Topic: Double integration over a region R

Q: Evaluate the integral: T So sin(x)dx

A:

Q: Use algebra and the properties of limits as needed to find the given limit If the limit does not…

A: We need to evaluate limit.

Q: Construct YOUR OWN example of how to determine the derivative of a given function and the process…

A: Given

Q: Question 3 Vx2 + 4dx 2²+4 Vx² + 4+ 2 In + C ava? + 4 +2 ln + C eva? +4 – 2 ln +C -글av고 +4-2n +C «…

A:

Q: 3. Cylindrical Method a. y = 9 – x2,y = 0, about the x – axis b. y = Vx,y = x, about x – axis

A: Given

Q: Express the slope of each diagonal line (the one side of each shape which is not horizontal or…

A:

Q: Q4) Find the largest eigen value for the matrix 1 2 A= with x" (0) =(7/17 1) 5 4

A: simply find eigen value of the matrix A , two eigen value of the matrix

Q: Let D be the region bounded by a curve x + y3 D (Parametrise the curve so that y/x t.) 3xy in the…

A: Given that D is the region bounded by the curve ?3+y3 = 3?y. The curve is to be taken as y/? =t.…

Q: f f(X) = sin 2x then f(X) = CoS (2x) f f(X) = sin 3x then f(X) = -3 cos (3x f f(x) = 2 cos x then…

A: a. Given f(x)=sin2x   Then f'(x)= 2 cos2x    B.   F(x) = sin3x       F'(x)= 3 cos3x

Q: (x-2)² y² =D1 5) %3D 81 36

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 5. Find the first six terms of the sequence in which the eighth term is 72 and twelfth term is 96.

A:

Q: Q1: Define each of the following b) Normal group c) Nilpotent element d) Prime ideal e)Field.

A: Define each of the folowing:- b) normal group c) nilpotent element  d) prime ideal e) Field

Q: [² + y²) dA; R = {(r,0):0 srs 4,0 s 0 < 27}

A: