If x + 1 f(x) then find the global maximum of on the interval [1, c0) Write DNE if there is no global max.

Q: (a) Use Green's Theorem to find the line integral over the simple, closed curve C : r(t) = (cos t,…

A: To use green's theorem to find the given line integral over the curve C

Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y= 0, y = 7+a*…

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Q: Represent the plane curve by a vector-valued function. x2 + y2 = 36 r(t)

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Q: 2 | (sin³x cos x + sinxcosx)dx 7/2 π

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Q: The sixth term of a geometric sequence is 1215 and the third term is 45. Find the first term and the…

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Q: *+ 2y = te-2t, y(1) = 0 2. Solve the IVP: dt

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Q: Evaluate the double integral over the rectangular region { 2(* sin(1) – y sin(z) dA; R= {(x,v) : 0 <…

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Q: 3 19. S Vy tan" Jy dy Ans. 2/3 n-"-2+ln 2 |

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Q: Consider the matrix -8 A = 13 21 1 4 -2 15, Where a;, represents the entries for A, for i= 1,2,3 and…

A: Given,        -8    0    5 A= 13    21  1         4    -2   15 a ij represents the entries for A,…

Q: Find the limit. lim (t i – 3 j+ t?² k) t-2 lim (t i- 3 j+1? k) = j + i i+ i i k

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Q: Find the general solution: y" + 4y' + 6y = 0.

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Q: Find the general solution of the differential equation. dy = xy + 3x dx

A: To find the general solution of the following differential equation.dydx=xy+3x

Q: Ex: Investigate the convergence of the following series. H.W 1 7 2) ΣΥ-1 3n 2n+5n IL !

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Q: e-2x 2+x In 3x csc' x -) f(x)=. b)Use logarithm to differentiate: y = (3х-1)

A: a)f(x)=ln(3x)csc2x-x5e-x3f(x)=sin2x. ln(3x)-x5e-x3differentiating w.r.t…

Q: 1. The study of integrals in calculus is motivated by the problem of calculating (a) the slope of a…

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Q: Find the indefinite integral and check the result by differentiating. Determine an appropriate…

A: Solve the given intregal

Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 1. (3xy + 3y – 4)dx + (x + 1)…

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Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 3. Vdx + (2x +1 – Vx)dV = 0

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Q: x2 - 8 R2.1 J x2 + 5x + 6 Answer with text and/or attachments

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Q: d d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (7t + 3)i + tj, 32

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Q: 4z² + 5dz 금(122+5) xo 4a? + 5 Part 2 of 2 ewrite the integrand in terms of u so that the integral…

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Q: Find the derivative of the following function by applying the appropriate derivative rules. f(x) =…

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Q: Utilize the Lagrange multipliers method to maximize the function f(x, y) = 8x + 18y - 10x2 - 4y2…

A: The given function is  f(x, y) = 8x + 18y - 10x2 - 4y2…

Q: 6. Find the indefinite integral. S 3x³ V3x4 + 7 dx (Use substitution method)

A: Solving the problem by finding the value of integration.

Q: Which of the following angle measure (in degrees) is coterminal to an angle of measure -690 degrees?…

A: To find a positive and negative angle co-terminal  with a given angle , you can add and subtract 360…

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: I have stated the used formula in the solution

Q: 5. Differentiate with respect to x: SET A. 5e

A:

Q: What is the period and domain of the basic cotangent function y= cot(x)? TT, {x €R|x=kT, kEZ} B 2 C)…

A: We can solve this as follows:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. P…

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Q: 21 The function f(x) is represented in the following table. Give the best estimate for f(x)dx 3 9.…

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Q: 2x (x- 3)2 .

A: Given: ∫2xx-32dx

Q: H.W (5) Solve the following differential equations of (x'+y')dx+(2xy cos y)dy phee

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Q: Given the expression below, y = ecos arc sec(ln(r |- determine y.

A: The derivative is given below

Q: Find the equation of the tangent plane to the graph of f(x, v) = In (17x² – 14y²) %3D at the point…

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Q: Find the sum of the first 21 positive integers. The sum of the first 21 positive integers is

A: We will use the concepts of A.P.

Q: Find the vector equation for the line of intersection of the planes x – 5y + 2z = 1 and æ + z = 1 |…

A: To find the vector equation of the line of intersection of given planes.

Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→∞ x2

A: We can solve part in the following steps.

Q: Calculate r'(t) and T(t), where r(t) = (2t – 5, 4 – 4t, 1 + 4t). %3D r'(t) = { %3D T(t) = {

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Q: A model for the length of daylight (in hours) in Philadelphia on the tth day of a particular year is…

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Q: (-1)"2"x" n=1

A: We will use ratio test to find radius of convergence.

Q: 4. SET A. Evaluate di/dt, correct to 4 significant figure, when t 0.1 and I 15t sin 3t. %3D

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Q: 3+ 12x4 – 7x +x³ a) lim 2л2 — За3 + х — 424 3x3 +x – 4x4* - -

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Q: Evaluate the following indefinite integral: x dx 1.) S- Vx4 - 1

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Q: Let be A, B, C three matrixes 30 1 B = z A = 2 y C = 5 13 -10, 10 What is the value for X that…

A: We will solve for x.

Q: is an angle in standard position, tan(e) 0, then the terminal side of lies in which quadrant? A IV…

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Q: 4. Given that sin 0 =- and let 0 be in second quadrant. 3 7 Find the values for all six…

A: A detailed solution is given below

Q: xdy + (y – cos x)dx = 0, y (- = %3D

A:

Q: x+x-6 lim X-2 x-2

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

Q: Given the linear differential equation: y'' - y = cos(x) - 5sin(2x) Find the general solution…

A: Solving