Find an equation for the line tangent to the curve at the point defined by the given value oft. Also, find the value of - at this point. x=t- sin t, y= 1– 2 cos t, t= 3 Write the equation of the tangent line. y =x+ (O (Type exact answers, using a as needed.) What is the value of at this point? dy (Type an integer or a simplified fraction.) 2 dx

Q: sin(3x) dx 1+cos²(3x)

A: The given integral is Sin(3x)/[1+cos2(3x)].

Q: Question 28 Find T, N, and B for the given space curve. r(t) = (In (cos t) + 8) i + 7 j + (5+t) k,…

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Q: -Find Taylor or Maclaurin for the following functions: 1) f(x) = sin 3x

A: In this question we can find the Maclaurin series for the function. Maclaurin series for the…

Q: Find the polar equution for the cartesian curve r=8 sin o Cos o r=8 sec e tan E r=8 sine tan E r=8…

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Q: 4. dr 4-

A: Given: ∫02x34-x2dx

Q: -3 2. (2x+4)3 8x dX use integration by parts and then find the value of definite integral.

A: A detailed solution is given below.

Q: 25. z arctan r dr dr 26. Jo (z – 1)² 27. e sin z dr

A: A detailed solution is given below.

Q: Solve the differential equation. f'(x) = 10x – 12.3 f(3) = 2 -

A: Given query is to find the solution of the differential equation.

Q: 5 and 6 8 and the angle between a and b is 0 = 75°. Given a a. Construct a well labelled diagram for…

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Q: Question 14 Find the volume of the indicated region by an iterated integration. The region that lies…

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Q: ving limits. Since you

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Q: B)号 4. nこt u puyと いつ0o Sinlen)+ w!l いo an

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Q: Find V x (V x F) if F(x, y, z) = 9xyj+ 5xyz k. V × (V × F) :

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Q: Identify the type of surface represented by the given equation. 2 O Parabolic cylinder O Ellipsoid O…

A: We know that x-h2a2+y-k2b2=1 is the ellipse standard equationGivenx27+y22=2Divide 2 on both…

Q: Two hours after the start of a 100-kilometer bicycle race, a cyclist passes the 74-kilometer mark…

A: Solution is done in step 2

Q: 14) f' (x) =(sin 3 x)'=, A) – 3(cot2 x) csc2x C) 3(tan2 x) sec2x By Power Rule B) – 3 sin2 x cos x…

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Q: 5. lim x-0 e2x-1

A: LetL=limx→ 0xe2x-1Plug in the value x=0L=0e2(0)-1L=01-1L=00Therefore Apply L Hospital ruleL=limx→…

Q: Question 15 Find the curvature k and radius of curvature R for the curve at the given point. y = sin…

A: The given curve is y=sin2x we have to find curvature and radius of curvature for the curve at the…

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Q: Evaluate the integral 7x sin y dy dx. 00 The value is (Type an exact answer, using x as needed.)

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Q: 1.) Find the area bounded by the curve y?= 1 - x and 2y = x + 2 2.) Find the area bounded by the…

A: Solution is given below:

Q: 465.98 23.98 2.789 56.09 ATATA TTA TA

A: Rounding up

Q: 28) In Problems 28 and 29, given the IMPORTANT FORMULA x(a+1)+ C (if a2 -1) and x1 dx = In x + C.…

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Q: dy_ y -1 dx

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Q: Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify…

A: Here, the area bounded by the curves y=4+x, y=0, x=0, x=16 is given by: A=∫016∫04+xdy dx

Q: Question 24 Solve the problem. Calculate the volume of the parallelepiped with edges a = (2, 4. 1),…

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Q: 19. e dr dr 4 – 2² 20. dr 21.

A: 19.)∫1∞e-xdx=-e-x0∞=-e-x0∞=-e-∞-e-0=-0-1=1∫1∞e-xdx = 1

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Q: Without graphing, find the horizontal and vertical asymptotes, if any, of the curves. Show your…

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Q: III. Do as indicated showing the details of your work. Show your complete solution on the space…

A: We need to evaluate definite integral.

Q: dx V1-e2x

A: A detailed solution is given below.

Q: Solve the following differential equations of dy 1 y= xy'; dx x

A: To solve the following differential equation

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Q: Use a triple integral to find the volume of the solid shown in the figure. z = 16 – x2 - y2 130 10…

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Q: Find T(t) and N(t) at the given poi: x = e cos t, y=e' sin t, z = %3D %3D T(0) = N(0) = %3D

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Q: Use a triple integral to find the volume of the region bounded by z = 7x + 8y, z = 9, and the planes…

A: Let's find.

Q: tanx dx I+x?

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Q: 1. Given ā = 31 -9j and 5 =-6i +j compute each of the following. (a) 105 (b) 14ã + 205 (c) 85- 2.…

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Q: NOTE: Enter the exact answer. xe*y dy dx

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Q: Qg Solve: coshx-1 .dx

A: Basic hyperbolic identities are used along with integration identities.

Q: Question 20 Evaluate the integral. TT/4 (8 cos ti +9 sin tj) dt -TT/4 O 9N2 i O &2 i+92 j O &V i

A: Topic = Integration

Q: Solve the following differential equations of 03B (1+x* )(dy – dx) = 2xydx,

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Q: 4. lim (sinx)tanx X0+

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Q: 0 1 2. (x + y + 1)dxdy -1 -1

A: Integral

Q: 2. lim (ex – 1)lnx X0+

A: (2). The given limit is: limx→0+ex-1lnx As we know that, the second indeterminate form is: ±∞±∞ ;…

Q: Question 15 The price per barrel of crude oil can be approximated by the function, P(t) = 0.45t? -…

A: We have to find the average rate of change of function.

Q: Solve the area bounded by the curve y = 4x - x² and the lines x = -2 and y = 4.

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Q: Q-What is the volume of the solid obtained by rotating the region bounded by the graphs of y = vx, y…

A: Volume of solid of revolution

Q: -2x (1+ee) dx e

A: