P 1. (1 Use the cylindrical shell method to find the volume of the solid obtained by rotating the region bounded by the following curves about the x-axis. y = √√x, y = x.

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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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: Find all points where the function has any relative extrema. Identify any saddle points. f(x,y) =…

A: f(x, y) =4x2+6xy+3y2-4x-8 In this question, we need to find all the points where the function has…

Q: 1. Why is it important to use the six trigonometric ratios in getting a missing angle value?

A: The six trigonometric ratios are sine, cosine, tangent, cotangent, secant, and cosecant. Basically,…

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

A: ∫1x2+a2 dx =1atan-1xa+C

Q: २ -2 el dy ely +2 e. 2

A: To integrate.

Q: 3. +∞ 8 -∞ dx x² + 1

A: Given ∫-∞∞dxx2+1To evaluate the integral:

Q: 9. A child is flying a kite with a 45-ft string at an angle of elevation of 50°. Which of the…

A: Let's find altitude of the kite in feet.

Q: cos³ 3x sin 3x dx

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Q: Determine the order of the given differential equation and state whether the equation is linear or…

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Q: Find the area bounded by the curve y = coshx and the x- axis from x = 0 to x = 1. a. 11.75 sq. units…

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Q: If F(x) = = [₂√₂ x² a. F'(1) b. F(2), by interpreting F(2) as an area √4t - t² dt, evaluate the…

A: Given: F(x)=∫x20 4t−t2dt To find : F'(1) and F(2)

Q: S 1 C=S²x + Sin'x

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

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Q: 1.) +y=e+ dx=3e-t 2. .) d- given: x(0) = 0, y(0) = 1 dy-x=0 d+y=1 given a z (0) = -1, y(0) = 1.

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Q: Nxx X-√√x 3 olx

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Q: III. Let f(x) = 2 sin x 1. Use the local linear approximation of f at x = 0 to approximate e2…

A: Given problem:-

Q: II. Evaluate the following integrals. 3. ²|2 - 2º| da

A: Given: ∫03|2-2x|dx

Q: For the function f(x,y) = 3 x³ + 5y4 5 4 x +y find f, fy, f(-1,1), and f,(-3,2).

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Q: 4. (x³ − 2x² + 1)dx [³ (x² - 2x + 5)²

A: The integral to be evaluated is ∫x3-2x2+1dxx2-2x+52. The first step will be to do a partial fraction…

Q: Jill burns 100 calories per hour while sleeping, 300 calories per hour while walking, and 200…

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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: A rock thrown vertically upward at a velocity of 24 m/sec reaches a height of s(t) = 24t - 0.8t²…

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Q: a. Arc length of the curve y = 4- (x-2)² 4 bordering the region R

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Q: Find the area in square units bounded by the following: (Show graph and detailed solution. Box final…

A: Here, the area bounded by the curves: y=x3+1 and x-axis  with the limits x=0 and x=3 is:

Q: What is the y-coordinate of the centroid of the plane region bounded by the x-axis and the…

A: Given

Q: Using the Ring or Washer method, what will be the equation of the volume of the solid formed when…

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Q: Find the volume of the sould generated by revolving the area bounded by the _given curves about the…

A: Let's find volume of solid (V) = ?

Q: Find the area of the region bounded by the curves y = the x-axis using vertical strip. (x+1)2/ = 4…

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Q: What is the second derivative of y = 6x² 3x³ + x² - 5 ? - Oy"= 72x² 18x + 2 Cinema) Oy" 24x³9x² + 2x…

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Q: Perform the integration. 3 [² (13² - 11 + 13* - 31) dx

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Q: Evaluate the limit using the L'Hopital's Rule. 1 - cosh x lim x→0+ ln(x² + 1)

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Q: Daniel saved $260 at the end of every month for 4 years in his bank account that earned 5.60%…

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Q: Perform the integration. (sinh x)(coth? x + csch3x) dx

A: Here is the solution:

Q: 6. How many outfit combinations can be put together from 6 shirts, 3 pairs of pants, and 4 pairs of…

A: Total shirt = 6 Total pants = 3  Total shoes =4

Q: 8. Find the area of the region in the first quadrant bounded by the curves y = sin x, y = cos x and…

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Q: equences . Given that a₂ = 6 and as 96 are terms of a geometric sequence, find a. 2. Given that a10…

A: solution

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

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Q: 3x² - 6x² + x (36²-6x² x)]d² X

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

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: Find the solution of the given initial value problem. ty' + 4y = t²t+7, y(1) = 5, t> 0 Y ||

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

A: We sketch the given region using a graphing calculator as shown below:   The shaded region is…

Q: Why is it =10πr33? particularly, why is the value 33?

A: Let's solve.

Q: Use the Second Derivative Test to find all relative extrema. (a) h (x) = x - 2 cos x, [0, 4π]

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Q: 2.) Obtain the solution of the following initial value problem! (t-2)x' - x = 2(t - 2)², x(0) = 1.

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Q: 0 sinx + 2cosx 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: lim x++∞ x² + x e²x + In x

A: To Find: limx→∞x2+xe2x+lnx