44. A tangent at the pole to the polar curve r = 2- 4 sin 0 is af pole 0 = = D 0 = Sing 8sin

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <: sos

A: See the attachment

Q: 4. Sketch the curve of r2 = cos 20 and find the area that encloses it. Show your complete %3D…

A: Converting polar coordinates to rectangular coordinates  Put r=x2+y2,  θ=tan-1yx in r2=cos2θ…

Q: Find the slope of the tangent line to the r=2-3cos 0 in polar coordinate at 0 =

A: Given:-r=2-3cosθdrdθ=3sinθTo convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y)…

Q: Consider the following parametric equation.  x = 18(cosθ + θsinθ) y = 18(sinθ - θcosθ) What is…

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Q: Find the derivative dydx of the polar function r=1+sinθ at θ=π4.

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Q: Find the expression for the tangent slope dy/dx for points on the Polar curve r= 6 +12 cosθ

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Q: What is y2 = 3x in polar form? r = 3 sin 0 sin 0 O Option 4 r = 3 csc 0 cote Option 2 r = 3 sin 0 -…

A: Given y2=3xTo find polar form:

Q: Consider the polar curves C, : r= -3 sin(20) and C2 : r= 3 sin 0. 3/2 3/2 (a) Find the equation of…

A: The given graph and point 322,322 To find the curve, on which the given point lies.  Find 'θ'θ =…

Q: Find the slope of the tangent line to the polar curve r = sin(70) at 0=. Enter as an integer or…

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Q: Find the slope of the tangent line to polar curve r = 6 – 9 sin 0 at the point (6-

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Q: Eliminate the parameter to find the cartesian equation of the curve: x = 2 sin 0, y = cos² 0, sos…

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Q: (a) (., Consider the curve defined by ry = In(3x + sin(y)). Use implicit differenti- ation to find…

A: Consider the given equation of the curve, xy=ln3x+siny Use the implicit differentiation,…

Q: 4 Find the slope of the tangent line to polar curve r = 7 – 4 sin 0 at the point ( 7 - - 2' 6 Submit…

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Q: Determine the slope of the tangent line to the polar curve r = 1 + sinθ at θ = π/4.

A: Explanation: Given that,  r=1+sinθat θ=π4     Concept used: To determine the slope of the tangent to…

Q: Consider the curves:r = 4sin 0 and r = 2 sin(0) + 2cos (0).

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Q: Consider the following parametric equation. #20(cos 0+0 sin 0) y- 20(sin 0-0 cos 0) What is the…

A: Given: x=20cosθ+θsinθy=20sinθ-θcosθ we know length of curveL on interval a,b is given by…

Q: Find the slope of the tangent line to the polar curve r=2cos0 at O %3D 4

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Q: 5(a) Find the slope of the tangent line to the polar curve r = 2sin0 -3cos0+1 at 0= 1/4

A: Using slope formula we have

Q: 2. What is the arc length of the polar curve r = 1- sin 0 for 0 <0< <5? 2 (a) 2(v2 – 1) 2 - V2 2/2…

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Q: Find the slope of the tangent line to polar curve r = 8 – 7 sin 0 at the point (8 %3D 2' 6

A: Given the equation of polar curver=8−7sinθ       .......(1)(8−72,π6)

Q: 9. Show that the curve with parametric equations x = sin t and y = sin(t + sin t) for 0st s 2n has…

A: Given that the curve with parametric equations are x=sint,y=sint+sint. First find the slope that is…

Q: 6. Find the slope of the tangent line to the polar curve r = 2 cos 0 when 0 %3D You may use sin ,…

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Q: 4.2. Calculate the arc length of the cardioid given by r = a(1 – cos 0) -

A: The cardioid is symmetrical in nature and ranges from θ=0 to θ=π as a half figure. We can also…

Q: Consider the curve with polar equation r= 6 sin where 0 <0<. Without finding the Cartesian equation,…

A: Given: The given polar equation is : r=6sinθ where 0&lt;θ&lt;π. To find: We have to determine the…

Q: Suppose a curve is traced by the parametric equations 3(sin(t) + cos(t)) = x у 3 18 — 6 соs"(€) — 12…

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Q: п 4. Find the slope of the tangent line to the polar curve r = 1 – sin40 at 0 = 4 : a. 3 b. 4 c. 2…

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Q: Find the slope of the tangent line to polar curve V3 T r = 4 – 6 sin 0 at the point 4 – 6 Preview

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Q: dy dx Given that r= cos 0 ; do - sin 20 and cos 20. de = - The slope of the tangent line to the…

A: Explanation of the answer is as follows

Q: Find the slope of the tangent line to the polar curve r = cos(e) at e =. Enter as an integer or…

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Q: 3. Consider the curves: r 4sin e and r = 2 sin(8) + 2cos (0). =

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Q: determine the slope of the tangent line to the polar curve r = 3 + 8 sin 0 at 0 =

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Q: Find the points (z, y) at which the polar curve r = 1+ sin(0), – sos has a vertical and horizontal…

A: The polar curve is r=1+sinθ. Suppose that x=rcosθ and y=rsinθ. That is,…

Q: Prove that L" (coshat sinat + sinhat cosat) %3D s*+4a*. 2a

A: The function F(s) is Factorize the denominator

Q: Find the points (x, y) at which the polar curve r = 1 + sin(0), – < 0 has a vertical and horizontal…

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Q: Find the slope of the line tangent to the following polar curve at the given point. 3x r= 3-3 sin 0;…

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Q: Find the points (x, y) at which the polar curve 8 cos 0, has a vertical and 3 horizontal tangent…

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Q: 44. The furthest point from the pole to the polar curve r = 2+ V2 sin 0 occurs when 0 = A. в о C 2

A: Answer

Q: Find the points (x,y)at which the polar curve r=1+sin(θ), −π/4 ≤θ≤π/4  has a vertical and horizontal…

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Q: Plot the cissoidr 2 sin 0 tan 0 and show that its equation in rectangular coordinates is x3 y2 2 - x

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Q: Find the slope of the tangent line to polar curve r = 8 sin 0 at the point

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Q: 3) Find the exact length of the curve. y = In(cos r), 0 < x<

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Q: 3. Let r = 1+ sin(0). Determine the rectangular point(s) (x, y) where the polar curve has a…

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Q: 15) Find the slope of the tangent line to the given polar curve at the point specified by the value…

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Q: Given that r= cos 0 ; dx = - sin 20 and de dy = cos 20. do The slope of the tangent line to the…

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Q: 9. Find the slope of the tangent line to polar curve r = 9 cos 0 at the point 2' 3

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Q: 3. Determine the arc length of the polar curve r= 2-2 sin0.

A: Given: r=2-2 sin θ   ……1

Q: Find the slope of the tangent line to the polar curve r = 2sinθ +1 at θ= π/4 and then find its…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.