Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis. y = √x 500k 3 5 10 15 20 25

Q: * Evaluate (if possible) the six trigonometric functions of the real number. (If not possible, enter…

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Q: J 3x - 2 4x² + 4x + 17 dr

A: Breaking the numerator is the key here. After that, break the given function into two parts and then…

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Q: 8. X lim 2 xxx +8x

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Q: 2. Evaluate the following and give the exact value: •TC/2r cos y TC-Y π/6 0 y sin (y tz) dz dx dy

A: Topic = Integration

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Q: Given the differential equation (4x2+y2)dx + x(x-2y)dy = 0  1. Verify that M(x,y) = (4x2 + y2) and…

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Q: 2. Evaluate the following and give the exact value: π/2 cos y are the (sin(y + 7) dz [** dx dy

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Q: Solve fz¹0 In(x) dx using Integration by Parts. Use u = ln(x) and v' = x¹0

A: We need to solve the integral ∫x10lnxdx using by parts.

Q: x)dy. А. у-е в. уте

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Q: II. Show that lim (x,y) →(0,0) x6 + 2y² does not exist.

A: We will show that following limit does not exist.

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Q: 1-(SXOM) 2

A: Find the value of (w^0x^5)^-1

Q: 2. Let A = a₁ + a2j + a3k and B = b₁i + b₂j + b3k. Then (A × B) . j is equal to a) a2bვ — a3b2 b)…

A: A=a1i+a2j+a3k B=b1i+b2j+b3k.

Q: (2). 크 2 2 5

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Q: Directions: Find the derivatives using the definition of limits (4-step Rule). Show each step from…

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Q: 56. S 1 √x² +9 dx

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Q: Subject: Differential Equation Use HOMOGENEOUS DE. Please have a clear and detailed solution.…

A: Given : rewrite

Q: 4. lim tan-¹ 818 X

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Q: Determine if the pairs of vectors below are "parallel", "orthogonal", or "neither". a = (-1, 1, -2)…

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Q: Suppose you wish to retire at the age of 65 with $90,000 in savings. Determine your monthly payment…

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Q: Solve the following quadratic equations using elimination method: Question 7: x2 - 4 - y = 0 x2 - 4…

A: Given, y= x^2 - 4 equation no.(1) & y= x^2 - 4 equation no.(2) Now, using elimination method.…

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A: To find out the peak of mountain for the given atmospheric pressure.

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Q: Find the average rate of change of the function f(x) = x² + 9x from x₁ =2 to x₂ = 5. The average…

A: As we know that; The average rate of change of the function fx between the interval x1≤x≤x2 is given…

Q: Element X has a​ half-life of 12 days.If we currently have a 29 ounce sample of Element​ X, how long…

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Q: 4) Find the surface area obtained by rotating y = t², t€ [1,4] about the y-axis.

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Q: 16. (x-ylny + y lnx) dx + x(lny - Inx) dy = 0.

A: see below the answer and calculation

Q: Suppose that the function fis defined for all real numbers as follows. 1+x² if x S Is the function…

A: Topic = Functions

Q: What is the angle in radians between the vectors a = (8, -1, -3) and b = (7, 7, -3)? Angle:…

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Q: -5 -4 -3 -2 -1 0-3 0-2 0-1 Do 01 5+ 4 3- 00 3 04 1 -1 -2+ -4+ -5+ Select all the x-values at which…

A: A function is not differentiable at x = k if  the function satisfies  any of the following…

Q: Solve for the determinant of the following matrix: 392 -2 8 5 02000 1-6 0-3 3 4 02 -8 5 00 3 1

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Q: Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the…

A: Recall: Disk method

Q: Set up the definite integral required to find the area of the region between the graph of y= 2² - 15…

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Q: Find the solution of each of the following initial value problems. -y=2te²t, (b) y' + 2y = te-2t,…

A: Note:-  As per your request i m solving part (a) from the given sub parts..

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x^4,…

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Q: Let T be an onto linear transformation from IR" to Rs. 1. What can one say about the relationship…

A: We have given that  T is an onto linear transformation from  Rr to Rs .

Q: 4. Evaluate the following and give the exact value: π/2 cosy -y π/6 0 'y sin(y+z) dz dx dy

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Q: Use the given conditions to write an equation for the line in point-slope form and in…

A: I am attaching image so that you understand each and every step.

Q: 2. lim tan x x 플 →

A: The given limit is limx→π2-tanx

Q: Integrate: dy/(-2-1.2y)=dx/(0.5+1.2x)

A: Given problem:- Integrate dy-2-1.2y=dx0.5+1.2x

Q: 3. (a) Find the slope of the tangent line to the parabola y = x² + 3x at the point (-1, -2) (i)…

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Q: 2) 2y(x² - y + x)dx + (x² − 2y)dy = 0 -

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Q: Part A: Use exact area calculations (not Riemann sums or the FTC) to evaluate of the following…

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Q: A tank holds 3,000 gallons of water, which drains from the bottom of the tank in half an hour. The…

A: NOTE: Refresh your page if you can't see any equations. . the given table is  t 5 10 15 20 25 30…

Q: Show that f is continuous on (-infinity, +infinity) f(x)= { 1- x2 , if x less than or equal to 1…

A: A function f(x) is said to be continuous at x=a if limx→a-f(x)=limx→a+f(x)=f(a).Also we know that a…

Q: 11. \mbox{If a particle's velocity is given by)\:v(t)--t+2\:\mbox (and its) distance at 1-2 is…

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Q: A loan shark lends you $90 at 2% compound interest per week (this is a weekly, not an annual rate).…

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Q: 8 3 ST 5 7 f(x) f'(x) -1 8 4 3 6 -2

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