Find the equation of the function f whose graph passes through the point ( 0, and whose derivative is 3 f'(x) = xV 4 - x2.

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A: Given

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A: 2)-(2x-3y) dx-(2y+3x) dy=0dydx=(2x-3y)-(2y+3x)dydx=3y-2x2y+3xdydx=3yx-22yx+3y=vxdydx=v+xdvdx

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Q: Let f(x) = 2x° - 6x - 48x + 8. a. Find all points on the graph of f(x) at which the tangent line is…

A: Here, the given function is: f(x)=2x3-6x2-48x+8

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Q: the radios of Cnvergente and the lInterval of conergence of the Pouer series (x-2)" n2 +1

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Q: Verify Green's Theorem by evaluating both integrals ƏN dA y? dx + x² dy = ay for the given path. C:…

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Q: Evaluate the definite integral. e6 i + e¯'j+tk )dt + (1 - 'e) -1(1 - م( ° e'j 6 -i- (e-' - 1)j+k i+…

A: We have to choose correct option.

Q: Use a double integral to find the volume of the region under the graph of f(x, y) = xy and above the…

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Q: 5. S (3x-x²)dx x2

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Q: ans 늘 sin ()+c 19 -4x² teinx dx I+ x2 dx ans: į sini'Ln'xte 3. sečxdx ensesin 3tanx 15-9tañx dx

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

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A: Given: y2=x and y2=2-x   Now find the point of intersection between the given curves. y2=x,…

Q: Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

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Q: Evaluate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

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Q: d Calculate ri(t) r2(t)] and rı(t) x r2(t)] first by differentiating dt the product directly and…

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Q: Find the limit V1+t4 dt lim

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Q: Determine the following limits, using oo or - o when appropriate, or state that they do not exist.…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t? + 7 lim t 612 + 7't 1° = (?, ?)

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Q: d Calculate ri(t) - r2(t)] and (ri(t) × r2(t)] first by differentiating d dt dt the product directly…

A: This is a problem related to vector's dot and cross product. Based on the rule of dit and cross…

Q: dx J (9x2-36)3 a. b. rV2-ezx dx ex V5+ln²x dx C.

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Q: Use the substitution u = x° + 8x to find the following indefinite integral. Check your answer by…

A: Use the substitution method to solve the integral.

Q: Use the Limit Comparison Test for 9n? + 25 Σ 00 Σ an = n(n n=23 12)(п — 13) n=23 to prove…

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Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is…

A: an=n45nlimn→∞ an+1an=limn→∞ (n+1)4 5n5n+1 n4=limn→∞ (n+1)4 5nn4  5n 5

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Q: 1. Find the derivative of the following. f(x)=13x* -7x²+5x²+11x+75 a.

A: Formulas:ddx(a f(x))=a ddxf(x)ddx(xn)=an xn-1ddx(a)=0;  where a is a…

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Q: Inn 1 1 1 1 + 25 1 1 a) Σ-(-1)" (- b) 1+ 4 1 + 64 n-Inn. 9. 16 36 49

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Q: Calculus

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Q: Eses: Find the derivatives of: 1 In sinx, 2 - sin(lnx), 3 - e-cosx 4 - /cos(3x - 1), 2 - [1+ cos(x?…

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Q: Solve using L.apiace transform: 2u – uz = xt, t> 0, u(0, t) = 2, u(x,0) = 1. %3D

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