Write a in the form a = a- T+ anN at the given value of t without finding T and N. r(t) = (t + 5)i + ( – 2t)j + ( – t)k, t= - 1 ... OT ON (Type exact answers, using radicals as needed.) a =

Q: 2) Convert the following rectangular equations to polar equations. a) x² - y = 3y b. 9xy = 1

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A: We have to find the maximum value.

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Q: 3r + cos r 2. Use Squeeze Theorem to evaluate_ lim 1-00 V1 +r2 - 5x

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Q: S(3x2 + 4x – 5) dx

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

Q: 2) f(x) =f"(x) 3 x+7

A: Use simple differentiation formula.

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Q: Find the second-order partial derivatives of the function. Show that the mixed partial derivatives…

A: Given: Now, fxx=∂2∂ x2x5+x2y2+y5+x+y    =∂ ∂ x5x4+2xy2+1    =20x3+2y2 fyy=∂2∂ y2x5+x2y2+y5+x+y…

Q: ul = 7,0 = 25

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A: Set the partial fraction decomposition of the given form

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Q: dx consider Using trigonometric substitution, find u ar (x²+x+1)½ (A) u=x+1, a=- (B u=x+1, a=1 C)…

A: Topic:- application of integration

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A: Given query is to find the equation of the line.

Q: e2 and x e*. Find the area below the curve f (x) = between x = %3D x In x

A: The region is bounded by the curve f(x)=1x lnx between x=e2 and x=e4

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Q: Consider the function f(æ) = 10,/T + 7 on the interval [2, 10]. Find the average or mean slope of…

A: This question can be solved using the concept of mean value theorem.

Q: (V9- x2 dx using Trigonometric Substitution what is dx ? x2 Consider 3 cos e de 3 sec e tan 0 de 3…

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Q: Evaluate the integral. 28) 335 B)- 215 A) 325 D) 36

A: Given:      ∫05  3x2 + x +6 dx

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A: Answer is in below step.

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A: We have to find the producers' surplus.

Q: tan (x) cos (x) 1 tan (x) +tan°(x) + C tan'(x)7tan?(x) +9]+ C 36 O 1 1 tan (x)-tan'(x) + C O…

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Q: X+ 6 2) lim х-6 (х-6)2

A: limx→6 x+6(x-6)2=6+6(6-6)2=120

Q: In how many ways can the digits in the number 8,400,000 be arranged? ways (Type a whole number.)

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Q: Using Integration By Parts,x: x dx = u v– Jv du X sec Svou -tanx - Jsec Find Ex tan 5 2 1. X sec x…

A: The given Integral is: ∫x sec 12x tan 12xdx

Q: Using Integration By Parts, x² Vx? +4 dx =uv- [v du Find Uv- du 3 3 2 -4)2 dx || 4 3 3 2 +4) 2 dx 3…

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Q: If ∫3 6 (5f(x)+2)dx=14, then ∫3 6 f(x)dx=

A: ∫ab fx±gx dx = ∫ab f(x)dx ± ∫ab g(x) dx

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A: The given function is: f(x)=x-log4x       =x-ln xln 4

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Q: -. Evaluate f. F dr where F(x,y, z) = e²i + xzj+ (x + y)k and C is given by r(t) = t²i + t°j- tk, 0…

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Q: Find the absolute extrema of the function on the closed interval. y = 4 cos x, [0, 27] Step 1 The…

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Q: evaluate indkfinite intersal

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Q: Given that A = (1,0,2) and B = (6, -2,3), solve for projąB.

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Q: x dx 24) (7x² + 3)5

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Q: C. ta the sum or the values of a and h such that f(x) - 2ax2 1 hr + 3 has a relative extremum at the…

A: 7.   The function f(x)=2ax2+bx+3 has a relative extremum at the point -1,2

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A: answer is in next step

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Q: 1. (32.12) Determine the radius of convergence and the interval of convergence n!(2a - 1)". n=1

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A: Topic:- application of integration

Q: A survey shows that a candidate is gaining votes at a rate of 2000t + 1000 votes per day, where t is…

A: Given problem:- A survey shows that a candidate is gaining votes at a rate of 2000t + 1000 votes per…

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Q: * tan°(x) cos“(x) 1 tan7(x) 1 tan (x) O tan7(x),

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