Find the centre of mass of the region between y = x x² and y = x³ from x = 0 to X = 1.

Q: 1 The equation z = 1 3 3 x² + y² is given in Cartesian coordinates. Convert the equation to…

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Q: j. lim sin x x →0 k. lim sin² x x→0 1. lim sin 3x X-Z 2 m. lim cos³ x X→= 2

A: To find:-(j) (k) (i) (m)

Q: Start with the geometric series (1) Σ nx", lx| < 1 n = 1 (a) Find the sum of the series nx-1, |x| <…

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Q: This problem finds the derivative of a function using the formal definition. The process is broken…

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Q: you alos calculate the following

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Q: Evaluate S 2x + 1 (4x + 3)(x + 1) - dx

A: Consider the integral

Q: The marginal profit in dollars on Brie cheese sold at a cheese store is given by P'(x) = x (20x²…

A: The given marginal profit function , where  is the amount of cheese sold in hundreds of pounds.The…

Q: 6. A particle moving with the velocity function v(t) = t²-3t+2,0 ≤ t ≤ 4. Find (i) the net distance…

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Q: Find ∫∫R(5x+2y)dA where R is the parallelogram with vertices (0,0), (-2,-4), (1,3), and (-1,-1).…

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Q: A model for the basal metabolism rate, in kcal/h, of a young man is given by the formula below,…

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Q: Find the ninth term of the binomial expansion. (p+q) ¹¹

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Q: What are the radius and the coordinates of the center of the circle with equation x2 +(y-2)2=30

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Q: Step 1 of 4 Find lim foo 10 3 Enable Zoom/Pan

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Q: Find the exact location of all the relative and absolute extrema of the function. (Order your…

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Q: Find the radius of conv- 00 n! n 1.3.5..... (2n

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Q: Evaluate ff xdxdy where R is the region bounded by x=2, y = 0 and y = x

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Q: S (x² − 2) dx; n = 4 32.

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Q: Suppose the cost to make a widgets is given by C(x) = 2x² + 4x + 2. Find the marginal cost function…

A: The given cost function

Q: 18. Find the volume of the largest right cylinder that can be inscribed in a cone of height 20.00…

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Q: Let g(z) = 6 Determine the most general indefinite integral of g. 1 6dz

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Q: 4. Find the derivative of the following functions: a. y = x² sin x b. y = ex cos x 3 c. y = (x² + 1)…

A: *Note – As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly…

Q: Hello, I need to evaluate the limits below but the grahp is made on paint, sorry about that.…

A: Given graph of function

Q: y² 7. Use a double integral to find the area between x = 2y and x = 3 Sketch this region.

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Q: 800 The demand function for a widget is given by p= 90+ where p is the price of the widget in…

A: The given demand function is,

Q: Let + f² f(x) dx = 3, Find S 4 f(x) dx = -10 5 ¹ [*³ f(x) – 6 and - 3 dx = f(x) dx = 3, [ f(a) f(x)…

A: The Sum Rule:The Power Rule:The Constant Coefficient Rule:

Q: 8. Find the linearization L(x) of f(x)=√√x² +9 at x = -4.

A: Given that the function

Q: Evaluate the following limits algebraically. 1. lim x--> - infinity   2x^2 / (x^3 + 5x)

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: 4. Solve Cauchy problem: y" - 5y' + 4y = 0, y(0) = 1, y'(0) = 2

A: To solve the following Cauchy problem.

Q: 5. If A = (611). 0 then eª = e e (8 €) e

A: A=

Q: L³₂x³dx -2 2 1 x+0.5 dx

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Q: Assume that y is the solution of the initial-value problem 5 sin x If y is written as a power series…

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Q: Consider the following integral. ƒ(9e¹) e* dx By making an appropriate substitution, the above…

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Q: Suppose limx→cf(x) = 5 and limx→cg(x) = -2. Find: a. limx→cf(x)g(x) b. limx→c2f (x) g(x) c. limx→c…

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Q: The system of differential equations : has the solution Y C₁ et V₁+ C₂ e¹₂ V₂ + C3 e¹³ V3 where (in…

A: Given that

Q: List the first five terms of the sequence. a1 = 5, 2n + 1 2an +4 а1 а2 аз ад a5

A: To list the first five terms of the following sequence.

Q: Find ∫∫R  −3x+5y/(x+6y) dA where R is the parallelogram enclosed by the lines −3x+5y=0, −3x+5y=3,…

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Q: he table gives the values of a function obtained from an experiment. Use them to estimate f(x) dx…

A: Consider the given table in the question.Given that n = 3&amp;#x25B3;x=b-an"…

Q: Given w = and ws. x² + y² + 6z Y x = sinp, y=p+ 3t - 4s, 2= t³ and p = 1-2t. Determine wt

A: Given that  ,

Q: Suppose that we're making and selling some widget and the cost (in dollars) when making a widgets is…

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Q: Find the exact area of the surface obtained by rotating the given curve about the x-axis. x = a cos³…

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Q: f 9 csc (2) sec (2) dx Evaluate the integral above by taking the derivative of each answer choice to…

A: We have integrate the given expression

Q: i. x+1 lim X→∞ X-1

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Please answer parts C and D

A: We have to find the limit of the given function.We will use the L Hospital rule to find the limit.

Q: Evaluate the integral: Ox= Ox= Ox= (A) Which trig substitution is correct for this integral? 0x= 0x=…

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Q: Find the equations of the tangent and normal lines to the graph of the function at the given point.…

A: The equation of the tangent line  to the curve y= f(x) at x= a is  The equation of the normal line…

Q: Which of the following is an appropriate choice for & when proving the following limit? Assume ɛ > 0…

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Q: 5. Calculate the following limits: x-5 a. lim x-5x2–25 b. c. d. lim x--5 x²+3x-10 x+5 t² +t-2 lim…

A: 5)a) limx-5 (x-5)/(x2 -25)b) limx-(-5) (x2 +3x-10)/(x+5)c) limt-1 (t2 +t-2)/(t2 -1)d) limx-(-2)

Q: The curve r(t)= (f(t),g(t)), where f and g are twice differentiable, has f'g'"-f"'g' curvature…

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Q: 2. The behavior of the system is a saddle. y' = -x + y, = -x-y

A: Given system is x' = -x +yy' = -x -y

Q: x = 2. (a) lim Below is the graphs of f(x) and g(x), and their tangent lines at YA y = 1.8(x-2) 0 x…

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