Given the curve in rectangular coordinates 36 = 1 16 Find the parametric equations given that whent = 0 the point on the curve is (6, 0) and a counter- clockwise rotation. æ(t) y(t) =

Q: Lesson 3.2. Derivative of a Function Activity 3.4. Use the definition of the derivative to find f'(x...

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Q: Sue wants to build an enclosed area behind her house for her pets. One wall of the enclosed area wil...

A: area of rectangle 

Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the giv...

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Q: Find the critical point(s) of the function f(x, y) = 6x²y – 12a2 – 3y? and use the second derivative...

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Q: Y and 2 Y if x dx? 七 and yo

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Q: Find all solutions to the equation |5-3x| -2 +x = 2x + 5

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Q: 1 1 f(x,y) = x² - 2xy + 3x +y? %3D 1. Compute the first- and second-order partial derivatives. 2. Fi...

A: Solution is given below:

Q: (x + y + z) dA. 3,

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Q: 5x4 dx x5-3 S4 cos (-3x + 2) dx [ 4cot 5x csc25x dx

A: You can solve these integral problems by using the method of substitution.

Q: 2. Find the derivative for each of the following, be sure to use proper notation and simplify when n...

A: As per guidelines I can only solve first three subparts , remaining can be reposted

Q: Confirm that the integral test is applicable and use it to determine whether the series converges. (...

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Q: Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in...

A: topic- trigonometric identities sin(a+b)=sin(a)cos(b)+cos(a)sin(b)

Q: A lighthouse rotates its light in a circular motion with a constant speed. If the beacon of light co...

A: Given ,  A lighthouse rotates its light in a circular motion with a constant speed If the beacon of ...

Q: Find the area of the surface generated by revolving the given curve about the y-axis. x = 2y + 3, 0 ...

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Q: Q: solve the equation 5 lim ( x-3 3y + 4x x - 3

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Q: Solve the triangle for which ZA = 30\degree, ZB = number. Do not use a decimal point or spaces in yo...

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Q: For the following function, a) give the coordinates of any critical points and classify each point a...

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Q: 3 - 2x? +x- 2 Use L'Hopital's Rule to evaluate Support your answer graphically. lim X2 x² +x-6

A: To find: The limit by L'Hopital rule. Given information limx→2x3-2x2+x-2x2+x-6

Q: If f(t)=2t+sin(t) describes the length of an oscillating spring in m/s, what is the instantaneous ra...

A: Solution is written in below steps.

Q: Determine whether the series converges or diverges. In(k) k k = 1 converges diverges

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Q: y" – 3y' + 2y = 0 y(0) = y'(0) = 1

A: We want to solve using Laplace transformation.

Q: Determine the volume of the solid obtained by rotating the region bounded by y= 2x2 and y = x³ about...

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Q: Select all vectors perpendicular to the vector (1,3, -5). (2, 1, 1) O (0, 5, 3) O (1, 1,3) O (4, 2, ...

A: Given query is to find the perpendicular vectors to the given vector.

Q: 03) Evaluate the following integrals: A) y = sec(tan-1x). tan³(tan-1x) 1+x2 dx

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Q: UQuestion 2| Differentiate each of the following functions with respect to x a) y = 3x b) f(x) = +5x...

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Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 00 5+ 2"...

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Q: 2. 조우 X*-xy y-3 Find van d

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Q: Fin d the intervals on which f (il I a creassing and decreasing are Con cave uP and con cave down an...

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Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: The given sequence,      17, 179, 1792, 1793,......

Q: 2. An electric current, when flowing in a circular coil of radius r, exerts a force kx F = (x² + r2)...

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Q: 48. h'(x) if h(x) 2+9

A: Here, the given function is: h(x)=e2xx2+9 To find the first derivative of h(x), using the quotient r...

Q: Eliminate the parameter to find a Cartesian equation of the curve. x(t) = 101nt y(t) = Vi (a) Cartes...

A: We need to eliminate parameter and find range for a and y.

Q: The derivative of the function y = cos(x ln 3)log3 (sin x) is:

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Q: Atmospheric

A: We will find the height of the mountain. 

Q: A function and its first and second derivatives are given. Use these to find each of the following. ...

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Q: Power Rule Give 3 examples with solution and final answer. Make sure it is unique and not advanced.

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Q: How to determine f(x) and g(x) for area between curves? So if I'm trying to figure out the area bet...

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Q: Use sigma notation to write the Taylor series about = xo for the function. In x; xo k =

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Q: 3 8. If sin e = - - and the terminal side of e lies in quadrant III, find cos e. 5 3 3

A: Topic  = Trigonometric ratios

Q: Verify that the indicated function y = Q(x) is an explicit solution of the given first-order differe...

A: Solution : when y=125-x2y'=-125-x22×-2xy'=2x25-x22y'=2xy2thus in terms of x,2xy2=dydx

Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. (...

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Q: Suppose that in a certain area the consumption of electricity has increased at a continuous rate of ...

A: topic- exponential function

Q: 2. Find the indicated limits of the following algebraic and trigonometric functions: x' -1 a. lim x ...

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Q: Find the derivative of the function without using the Quotient Rule. y

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Q: Y zo when X-0 -h sin TRX

A: topic - integration 

Q: Determine whether the series converges, and if so find its sum. 4k+2 Σ 7k-1 k=1 1) This series can b...

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Q: The derivative of the function y = tan(In(vx2 –- 6x + 1)) is: |

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Q: Find an equation of the tangent line to the graph of the function at a given point. Note: do not use...

A: Solution :we know that equation of tangent at a,b with slope dydx at that point.y-b=dydxx-a1. y=6x2+...

Q: 11

A: We will find the derivative. 

Q: xdy +(y– xy+2)dx = 0

A: The given differential equation is; xdx+(y-xy+2)dy=0