Find the are a of the region bounded by the given 1) sketch the area, ii) Determine the boundaries a and i1) set-up the definite integ rol iv) Integrate 2 3) X = 2y² and x = 4+ y ² curver,

Q: What is the volume in cubic units of the solid formed when the region bounded by y = 2x + 1, x-axis,…

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Q: The function f(x), which is defined for a ≤ x ≤ b, has the following behavior: f'(x) 0. Choose the…

A: Follow the procedure given below.

Q: Evaluate the improper integral or state that it diverges. P -dx Select the correct choice below and…

A: The given integral is: I=∫2∞32x2dx   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 And…

Q: II. Evaluate the following integrals. 3. 12-2² | dr

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Q: Determine the following integrals: 1.1.1 ļ (cos2x+sin x) dx x+1 .1.2 1₁ JF dx x + 2x+1 2 1.1.3 | ₁…

A: ∫ sin(ax) dx =-cos(ax)a+C       and     ∫cos(ax) dx =sin(ax)a+C ∫xn dx = xn+1n+1+C Note : As per our…

Q: Find the general and the particular solution: d²u du = 4(1 + 3v)²; u = -1,and = -2 when v = -1 dv²…

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Q: Evaluate S2² (2x + 3e* − ¹) dx a. 12.43 b. 13.45 c. 14.24 d. 15.23 e. NONE OF THE ABOVE

A: Given :∫122x+3ex-4xdx

Q: Stan5 x sec³ x dx

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Q: Find fx (x,y) and f, (x,y). Then, find fx(1, -2) and fy (-3,3). f(x,y) = -2xy +9y² + 10 fx(x,y)=

A: We can find the answer as below.

Q: Evaluate the following integrals. 1. S 1- coth² (log2 x) x cosh(log₂ x) -dx π 3 (sin³ x) VT…

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Q: Where is the sketch of the area?

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Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2, y = 1, and…

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Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

A: We need to find D.E>

Q: The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R'(x) =…

A: Here, R'(x)=(x+2)ln(x+2)

Q: Prove that d/dx(cos x) = −sin⁡ x using the definition of the derivative.

A: Given: fx=cosx   As we know from the definition of the derivative; The expression for the derivative…

Q: 4 fcos 3x sin³ 3x dx

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Q: y s 5 4 -2 -2 The diagram shows the shaded region bounded by the curves y = x² + 2, y = 4 - x, y = x…

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Q: Using the shell method, what will be the equation of the volume of the solid formed when the region…

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Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

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Q: Evaluate f(x³ -x + 1) dx a. 0.250 b. 0.500 c. 0.625 d. 0.750 e. NONE OF THE ABOVE

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Q: 2x x→∞ 3x² +5 3x xx√√√x² x² +4 X lim x→→∞ 2 sin î (a) lim (b) lim (c)

A: Given

Q: A small business determined that the price-demand and cost functions for producing and selling x…

A: We have to find the production for minimum average cost.

Q: I. Evaluate the following limits. sinh r2 → r2 1. lim z→0 sinhr 1

A: We will apply DL hospital rule more than once to solve this question.

Q: Determine the intervals on which the function is concave up or down and find the points of…

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Q: Set up the double integral that will find the volume of a solid bounded by z = 1- y²x² and the xy-…

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Q: A window has the shape of a square surmounted by a semicircle. The base of the window is measured as…

A: Given that a window has the shape of a square surmounted by a semicircle. The base of the window is…

Q: Find the lateral surface of the cone generated by revolving the line y = mx from x = 0 to x = 1…

A: Given

Q: Use the linear approximation to estimate In (√0.99).

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Q: What is the y = x^2 - 4 and x-coordinate of the centroid of the plane region bounded by y = 2x - x^2…

A: Here we have to find the x coordinate of the centroid of the area bounded by the curves.

Q: Perform the integration. TT 3 sec³x tan x dx 2 + sec x 0

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Q: Evaluate the limit: lim (x - ln x)* x→0+

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Q: 4. Which of the following lines is parallel to y = 6x 18? 3x+6y=2 ○ 2x + 3y = −2 -6x -6x - 2y 2y =…

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Q: Find the area bounded by y = sin √x and y = 0 on the interval [0, π^2].

A: The curves are y=sinx, y=0 on the interval 0, π2

Q: Determine the instantaneous rate of change of the function πt³ √x sin (TE³ 2 f(x) = x3 1 + √t at…

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Q: Find the solution of the given initial value problem. 2 cos t y' - - Y y (π) = 0, t> 0 t-2' y(t)

A: Given: y'-2ty=costt-2,       yπ=0

Q: DETERMINE THE INSTANTANEOUS RATE OF CHANGE OF THE FUNCTION AT X=1 sin (2³) 1 + √t - f(x) = x3 dt

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Q: X Let f(x,y) = 8 e + In (x+y). Find the following. (a) f(1,0) (b) f(2, -1) (c) f(0,e) (d) f(0, e 4)…

A: Note: According to our expert guidelines only first three subparts are to be answered kindly repost…

Q: Evaluate the limits using the L'Hopital's lim (tan x) (sin x-1) x+2+

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Q: What is the center of gravity of the solid formed when the plane region bounded by 2x+y-2= 0, y = 0…

A: Center of gravity is given.

Q: 3. (x³ - 4)dx x3 + 2x² + 2x S

A: Given, ∫x3-4x3+2x2+2xdx

Q: Find the absolute extremum points of f(x) = sin2 x + cos x on the interval [0, π].

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Q: Set up the double integral that will find the volume of a solid bounded by z = 1- y²x² and the xy-…

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Q: Perform the integration. x-1 S= dx x² + 5x + 8

A: ∫1x2+a2 dx =1atan-1xa+C

Q: e e (lnx)³ dx X

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Q: Evaluate ¹ dx √√9-4x2 a. 0.285 b. 0.123 c. 0.423 d. 0.365 e. NONE OF THE ABOVE

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Q: (x² - 12x + 9) dx (x²-3x + 2)² 2. √(x²

A: Given: I=∫x2-12x+9x2-3x+22dx   As we know that; The Power Rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: 4. Evaluate the double integral: So p 1/3 27 +1 (Hint: Change the order of integration to dy dx.) dx…

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Q: 3.2.2 Test for exactness then solve. y(2xy2 − 3)dx

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Q: Question 4 Given a second order differential equation d²x dx 2 + 10x = e²t dt² dt dx where t = 0, x…

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Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^3, y- axis,…

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