Find the rate of change in the area (A) of a circle with respect to its radius (r) when r = 9. 9TT 27T 81T 18T

Q: Find the volume of the region of R^3 bounded by the paraboloid z=x^2+y^2 and by the planes…

A: Concept: Let us take D to be a bounded, closed space region. Let a and b represent real numbers,…

Q: Complete the parametric equations of the line through the points (7,3,-5) and (0,6,1) x(t) = 7 - 7t…

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Q: Evaluate sec(log x) -dx x In | sec(log x) + tan(log x) | +C 1 log e In | sec(log x) + tan(log x) |…

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Q: 2dx 2 2 cos x√ 4tanx - tan x S-

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Q: If X(z) is the z-transform of the signal x(n), then what is the z- ?transform of the signal x(-n) x…

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Q: The position of a particle in space at time t is r(t) as shown below. Find the particle's velocity…

A: The position of a particle is r(t)=2 lnt+1i+t2j+t22k

Q: Question 4 (a) Solve the following: √4x¹dx (b) Explain with the aid of a sketch how this value can…

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Q: Use any method to determine whether the series converge. ∞ 1 (2) Σ 4k k=1 The series (5) Σ k=1 The…

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Q: Given the following vector field and oriented curve C, evaluate SF.T ds. C F= (-3y,3x) on the…

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Q: x³-y³ Determine whether the function z = g(x, y) = x² + y² (why or why not) for for (x, y) = (0,0)…

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Q: Suppose I want to make a simple garden with 3 plots (pictured below) out of wood. у If I have a…

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Q: Consider the function f(x): = 1 1-x²

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Q: Find the area of the surface that results when y= around the x-axis from x = 1 to x = 2 223 is…

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Q: Solve the following initial value problem for r as a function of t. Differential equation: -=…

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Q: If f'(x) = g'(x) for 0 < x < 1 then f(x) = g(x) for 0 < x True False

A: Topic:-  application of derivatives

Q: The height of a certain amusement park ride follows the function h(t) = −³+ 11t² — 32t + 28, where…

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Q: 17. 18. 19. dx/ (9x² + 4) sin³ x cos x dx (secs x) dx / csc x

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Q: Evaluate improper integrals if they converge, or 1/7 a) S. 72 de dx shab diverge

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Find an antiderivative F(x) of the function f(x) = 7 sin(x) such that F(7) -9. F(x)= = = Now, find a…

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Q: integral

A: We will find the solution m

Q: 4.1 Evaluate the integral [3√x √(3√x - 1 / +5 4 + x² expressions after applying the integration…

A: We have to evaluate the integral

Q: Evaluate using Partial Fraction Decomposition: (- 2. -dx

A: Use partial fraction to evaluate the integral

Q: Find a plane containing the point (5,-6,-3) and the line x(t) y(t) z(t) = = = - 4 - 7t 1 -8t 3 - 4t

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Q: ?What is order of the equation (y"+2y+3=0) Second order O First order O Zero order O Third order O

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Q: 1 Consider the function f (x) = on the interval X - 1, 1]. If the Mean Value Theorem can be applied…

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Q: Consider the initial value problem y' + y = 5 + 2 cos 2t, y(0) = 0. 4 a) Find the solution of this…

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Q: d=(-3,-2) and 6=(2,4). Represent a-6 using the head-to-tail method. Use the Vector tool to draw the…

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Q: y= 3x + 2 √2x³-1

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Q: y = esin(tan-¹ x)

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Q: Solve step by step in digital fe 6x - 1 a) lím x→ 1/ 2x - 6 b) lím X-00 x² - 9

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Q: EVALUATE S 4x²-x+4 x³+x²+2x+2 dx

A: A detailed solution is give

Q: f is continuous on (a, b) then there is a number c in (a, b) such that f(c) is an abso inimum value…

A: Topic:- calculus    Definition :-  Extreme Value Theorem   If a function f(x) is continuous on a…

Q: Evaluate using Partial Fraction Decomposition: S x² (x+1)²(x-1) dx

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Q: To test this series for convergence n n=1 √n² +1 8 You could use the Limit Comparison Test,…

A: We will solve this question using limit comparision test.

Q: Question 4 (a) Solve the following: 4x¹dx (b) Explain with the aid of a sketch how this value can be…

A: we have to find the value of integral ∫-22 4x4  dx

Q: 4dx 3r x-√√x² S

A: Let's solve given integral.

Q: Solve the following initial value problem for r as a function of t d²r Differential equation:…

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Q: Given the function f(x) = -2x + 6x within the interval [0,8], at what values of x do the absolute…

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Q: Solve the integral shown below. . S | xsin xdx

A: Given problem:- ∫x sin(x)dx

Q: KIN KIN 0 2 d2 sinr do dr dọ

A: A detailed solution is given below.

Q: √√3 L dx 1+x²

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Q: Use the transformations to graph the given function. Show all translations on each transformation.…

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Q: Determine using Cauchy Riemann equations the function below is analytic or not? f(2)=x² + y² - 2xy

A: This question can be solved using the concept of the two conditions of Cauchy Reimann for a function…

Q: lim-0 OI Oll O III OIV e² - x Not Indeterminate کے

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Q: Find the value of a which makes the function below continuous on (-∞, ∞). f(t) = [a(x²/2) x < 1…

A: We will use the definition of continuity to solve this question.

Q: Suppose f(x) = 3x² + x - 3x²+x-6. Compute the following: A.) ƒ( − 4) + ƒ(1) = = B.) f(-4)-f(1) =

A: Given f(x)=3x2+x-6f(-4)=3(-4)2+(-4)-6=3(16)-4-6=48-10∴f(-4)=38

Q: What is the derivative of y = log, sec(e²x) Dxy = 2 e² tan (²) Dxy = 2 (log, e) e²x sec(e) tan(e) D,…

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Q: 15. Use the results of problems 12,13 and 14 and assume that the Maclaurin Series expansion for ex…

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Q: Find the direction derivative of f(x,y)= Xe ² + y ² at the paint (2,1), by the dirction of V = i- j

A: Topic:- application of derivatives

Q: * The z-transform of a signal is given below,its final value Z-1 2-¹ (1-2-4) x(z) = 0.25 (1-z-¹)²…

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