a) [ i) Find the exact length of the curve y = x³ + 12x 1≤x≤2

Q: ∞<a=(a'l Find the local max & min using First and second Derivative 3 f(x) = 9+3x2 - 2x² 7 sou?

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Q: Without using a calculator, for the following, determine the definite integral that represents the…

A: Here, the given curve is r=3-4cos θ. The graph of the curve is: To find the area of the shaded(red)…

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Q: 1. Find the radius of convergence and interval of convergence for the series n=0 2nx" 3"

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A: The objective of the question is evaluate the sum of two series.

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Q: Find and classify the relative extrema of the function, if they exist. You MUST use the…

A: Given :fx=2xx2+1

Q: How many critical points the following function has, g(x, y) = x³ + x + xy²? Select one: CO None of…

A: Using partial derivative with respect to x and y ,

Q: The maximum value of the function f(x,y)=x+y-5, x² + y² = 2, is-7. Select one: subject to the…

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

Q: 27. A function on [0,2] defined by f(x) = -x² |5x – 4 4x³ 3x (3x + 4 - if x ≤ 0 if 0 < x≤ 1 1<x<2 if…

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Q: Evaluate the limit of a. 3 b. O tan 2x-2sinx as x approaches to 0. c. Undefined d. Infinity

A: As per our guidelines we are supposed to answer only one question. Kindly re-post other question as…

Q: I. Perform the indicated multiplication on the differential operator D. (D+2x)(D-3x)

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Q: If    f(x) = 2 cos(x),    0 ≤ x ≤ 3pi/4,    evaluate the left Riemann sum with  n = 6,  taking the…

A: Given :fx=2cosx   , n=60≤x≤3π4

Q: 3. A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a well…

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Q: II. Solve each of the given LDE of order n. 2. (D³ +6D³ +2D² - 27D+18)y=0

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Q: The Cartesian coordinates of a point are given. (a) (-6, 6) Find the following values for the polar…

A: Polar coordinates

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Find f'(x) if f(x) = -7x5 +4√x. f'(x) =

A: To find derivative f'(x)

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A: We have to find percentage rate of change

Q: Find the general solution of the differential equation y" - 10y + 125y = 0. NOTE: Use c₁ and ce as…

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Q: Given the region D in the first quadrant enclosed by x = 0, x = y², and y = 2. Express D as a region…

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Q: Question 2 [" a. Find the critical points of the function f(x, y) = 6x² - 2x³ + 3y² + 6xy. b. s]…

A: Extreme Points of Function f(x,y)=6x2-2x3+3y2+6xy

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Q: 13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3-2 Find an equation for the graph above. 5+ g(u) 4 3 2 - -2- -3-…

A: We need to find equation of given graph.

Q: Consider vector field: F = e i-cos y j+ sin² z k. Obtain divergence and curl for F at points (0,,).

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Q: Give an example of a derivable function f (x) with f ′ (- 4) = -3

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Q: 1. y (x²-y²2) dx + x(x² + y²) dy = 0

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Q: A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An…

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Q: Frogs have been breeding like flies at the Enormous State University (ESU) campus! Each year, the…

A: This question can be solved using the concept of exponential growth model.

Q: please solve d-f now. thanks.

A: We have to find the composition of functions.

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Q: Evaluate the integral and check your answer by differentiating. NOTE: Enter the exact answer.…

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Q: of. F. F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

A: We need to find integral.

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Q: Determine which of the vectors is (are) parallel to z. Use a graphing utility to confirm your…

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Q: Assume that x = x(t) and y=y(t). Let y = x³ +5 and dt Find dt dy dt when x = 3. (Simplify your…

A: Here is the solution:

Q: Choose the gradient of the function \(f\) defined by f(x y) √1 (4x 5y)². O None of the others 4x+5y…

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Q: Find f'(x) and simplify. f(x)= Which of the following shows the correct application of the quotient…

A: We can solve as follows Do not confuse in round bracket and close bracket. They are same in this…

Q: Question 2 [" a. Find the critical points of the function f(x, y) = 6x² − 2x³ + 3y² + 6xy. b. s]…

A: Given :fx,y=6x2-2x3+3y2+6xy

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. | sin (2) x²…

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Q: Find the area of the surface over the given region. Use a computer algebra system to verify your…

A: answer is in next step. please give a like !!

Q: 5. If f(x) = 2x² - 3 and g(x) = 2 sinx, determine (f • g)(x) and (ƒ • 9) (³7), 0≤x≤ 2π.

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Q: Find the equation for an exponential function that passes through the pair of points given below.…

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Q: Solve the system: (combined method) x² + 2xy-y² = 14 x² - y² = 8

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Q: Solve the problem. 15) Let f(x) = ex. Round to 6 decimal places as needed. a) Find the linearization…

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Q: Problem 6 convergent. The series is Justification: Determine whether the series n=110 is…

A: See this solution in below