Find the volume generated by revolving the given bounded plane area about the line. Use shell method. y = 2x², x = 0, x = 5, and y = 0, about the y-axis

Q: Question 9 Let f(x) f-¹(x) = 1 2+8

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Q: P(2,-3,4), Q(4,4,5), T(1,2,7) forms a triangle. find the vector projection of QP parallel on QT.

A: Proj. of QP→ on QT→ = QP→·QT→QT→WhereQP→ = Q-PQT→ = Q-T --------------------------------------------…

Q: π/4 x³ dx (x²+4)5/2 (Use trigonometric substitution)

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Q: (A) = and B D = . Find the vector projection of A onto 2A - BO O O O none of the above

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Q: x²+x+1 Sa 2x²+2+3+x A B cb dx g(x) - dx = [Aƒ (x) − B ln(g(x)] + D fb da, and if A = ‚B <0, then dx…

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Q: 3. S 2 x²+a² x4 = _ (x² + a²) ³² 3a²x3 -dx = + c

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Q: A B C The IBP formula fudv=uv-fvdu can also be written as f udv + ſ vdu : = UV Which of the…

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Q: π/4 x² dx (x²+4)5/2 0 (Use trigonometric substitution)

A: Given integral I=∫0π4  x3(x2+4)52 dx

Q: Explain why you think the sequence converges to a finite number or (n+1)! diverges. If the sequence…

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Q: V. Given: 2. Find f'(2), if it exists. f(x) = el32-61-2, [2x - 5], √x²-9, if x 3 14

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 3. Using trigonometric substitution, what is 1 sec-²¹ ( 137 ) + √x²-9 2x² + C A. 1 300² (2) √²-90…

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Q: 8. The integral What is the value of A. B. can be rewritten as 15x²x³43x - 19 (x + 1)²(x² - 6x +13)…

A: Let's find.

Q: Given The boundary of C: 0 ≤ x ≤ π,0 ≤ y ≤ sinx With Green's Theorem, Evaluate this line integral. $…

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Q: C. y = 5x² + 2, x=0, x=2, y = 0

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Q: List intervals on which the following function is INCREASING. Use INF for infinity, use no spaces,…

A: The given function,    fx=3x2-1

Q: Use the formula k(t) k(t) = = ||r'(t) × r"(t)|| ||r' (t)||³ = 10t: r(t) = e¹⁰ti + e-tj to find k(t).

A: This question is related to vectors, we will solve it using given information.

Q: Explain why you think the series Σ01 77 converges to a finite number (-8)"-1 or diverges. If the…

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Q: 15x² x3-43x - 19 - (x + 1)²(x² - 6x +13) Ax + B S ax²+bx+c The integral What is the value of dx can…

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Q: log(x+3) z-1-1-cosh(cos-12) 4. lim

A: Given,            limx→1-log12x+31-coshcos-1x

Q: * Evaluate. [12 [20x cos(5x² - 1)]dx

A: The given integral is   ∫20xcos5x2-1 dx We solve the integral using proper substitution .

Q: [w (1-32)] 3w 11. lim w In 1 In W→∞

A: LetL=limw→∞ wln1-23wFor L hospital L=limw→∞ ln1-23w1wNow apply L hospital ruleL=limw→∞…

Q: (D² — 4)y = 8e²x — 12 - -

A: Given; D2-4y=8e2x-12 So, the auxiliary equation is; m2-4=0

Q: Compute the area bounded by the curves x=2y² and x=4+y²

A: Area bounded by two curves x=f(y) and x=g(y) is given by, A=∫abf(y)-g(y)dy ,a,b are the points of…

Q: Sx² In²x² dx Integration by-parts

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Q: /² sin sin ( π/4 x² dx (x²+4)5/2 (Use trigonometric substitution) fe2x+Inx² sin x² dx = = Find f…

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Q: Using trigonometric substitution, what is A 1 6 sec-¹ (37) + √x²-9 2x² +C Ⓒ 3 sec ¹1( 3 ) + √x²³ - 9…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t² +4 1 = lim t→+∞0 (?, ?) 4t² +5't

A: limt→∞t2+44t2+5, 1t

Q: Y sinh(1) (use logarithmic differentiation) 3 (sec x)²/2[/cot-¹x]

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Q: 8 Given: (В © √³x³sin(2x)dx= F4 5T 6 21 Зд TL 277²-24 64 T Find bif sb st

A: Solution is given below:

Q: 7 4x + 10 Let f(x) This function has: 1) A horizontal asymptote at y = 2) A vertical asymptote at x…

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Q: 4d³y-13 +6y=0 dy dx3 dx

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Q: Identify the surface that corresponds to the equation 100y^2 - 25x^2- 4z^2 = 1. O elliptic…

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Q: Find the equation of the vertical asymptote and the equation of the slant asymptote of the rational…

A: Given: fx=36x2-12x+36x-3   As we know that; To calculate the vertical asymptote, equate the…

Q: √√√x²-9 Consider x³ what is the integral form in terms of? 1 A Scos²e de B Scos²e de Ⓒ-S sin²e de C)…

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Q: Find exactly T(1) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

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Q: Find the degree of the term 126: Find the degree of the term - 6: Find the degree of the term - 12³:…

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Q: IV. Do as indicated. 1 1. Let f(x) Find the equation of the tangent line to the graph of f'(r) at…

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Q: S Find sec42x -dx tanº2x cot²2x-cot82t+C 12 16 1 1 1 1 12 tan 62x 16 tan 82x --(cot$2x) (² 1+3csc²2x…

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Q: Sketch a graph of f(x)=(x-2)² +4 6.

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Q: Find a set of parametric equations of the line through the point (1,-2, 3) and perpendicular to the…

A: Concept: As we know that a equation of the line through the point (α,β,γ) and perpendicular to the…

Q: Sa 2x²+2+x³+x² =dx = [Aƒ (x) — B ln(g(x)] + D fb dx, and if A = ,B<0, then f(x) dx x+2 x² 2x + + 5…

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Q: Use the formula к(t) : = ||r′(t) × r"(t)|| ||r' (t)||³ 9t r(t) = e⁹ti + e-tj to find k(t).

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Q: 1. Let f(x) = Find the equation of the tangent line to the graph of f'(x) at the point x² + 1 where…

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Q: 9. The surface area of a cylinder is A = 2h+2². If the radius is measured to be 6 inches with a max…

A: Given, Surface area of cylinder, A=2πrh+2πr2 Given radius r=6in with maximum possible error dr =…

Q: 1. f/² sin (1) cos (4) Sir sin (²) dx (Consider initially the first 2 terms)

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Q: The phone company A Fee and Fee has a monthly cellular plan where a customer pays a flat monthly fee…

A: answer is in next step

Q: ♫♫¹⁄² sin (*) cos (*) sin (²) dx (Consider initially the first 2 terms)

A: Solving the definite integral.

Q: Find Duf at P. NOTE: Enter the exact answer. Duf = f(x, y) = sin(3x – 4y); P(4,3); u || 35 i I

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Q: Let f be the function given by f(x) = (In x)(sin x). The figure above shows the graph of ffor 0 < x…

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Q: Find the area of region bounded by the graphs of the equations. a. X b. y = x + sin x y + 3 2 1+ -R…

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