2. Eliminate the parameter and find the equation of the curve in x,y Curve: x=1-sin?t, y= cost, 0

Q: Eliminate the parameter to find a Cartesian equation of the curve. x=1-cos(t) y=1-sin(t)

A: We have to eliminate the parameter and find the cartesian equation.

Q: (1 )  (a)  Find two positive numbers x and y whose product is maximum and 2x+y=100. ( b )  Find…

A: a. Given The product is given by P=xy Plugging the values: For P to be maximum, the derivative…

Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter…

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Q: What is the equation of the line tangent to the curve ev + cos(x) = 1 at the point (,0*? Y = 0 A B…

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Q: (a) Find the slope of the tangent line to the parametric curve x = t/2, y = t 2 + 1 at t= −1and at t…

A:

Q: 1. Find the length of the curve given by e' (sin t+cos t) , yY = e'(cos t – sin t), x = 1<t< 4 .

A: The length of a parametric curve is given by L=∫abx't2+y't2dt Now, we have…

Q: A particle moves along the curve y=x3-x. If vx = 2 ft/sec and ax= -3 ft/sec2 as the particle passes…

A:

Q: 4. Find the acute angle between the curves y = sin r and y = cos r (0 < r <) at their point of…

A: We find the point of intersection by setting them equal

Q: Find an equation of the tangent to the curve given by = evi y = t – In(?) at the point corresponding…

A:

Q: 11. Find an equation of the tangent plane to the surface Va+Vy+Vz=4 at the point P(4,1, 1). 12. Find…

A:

Q: 3. Consider the parameteric equations for a curve C given by x(t) = cos t(1 – cost), y(t) = sin t(1…

A: Given that: xt=cost1−costyt=sint1−cost

Q: What is the point of intersection of the tangent lines to the curve r(t) = sin(πt)i + 8sin(πt)j +…

A: Let us consider the given curve r(t) the tangent line is obtained as Find the derivative of the…

Q: Find the length of the curve. r(t) = cos(2t) i + sin(2t) j + 2 ln cos t k,     0 ≤ t ≤ π/4

A: Consider the length of the curve is, r(t)=costi+sintj+(lncost)k Then,…

Q: can any thing said about the tengent to the curves y=sinmx and y= - sin(x/m) at the origion (ma…

A: Solution  Given

Q: Find the length of the curve y2 = ln x, -1 ≤ y ≤ 1.

A:

Q: 13. Eliminate the parameter t, sketch the curve, and indicate the orientation. x=5 sint, y= 5cost,

A: We will square the both equations and then we will add them to eliminate the t

Q: 1 2. Find the length of arc of the curve x = + from the point where y = 1 to the point where y = 2.…

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Q: ind the slope of the line that is tangent the curve sin(2x)+sin y=e*y – 1 at (0,0). our answer…

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Q: Find the exact length of the curve y = ln(sec(x)),   0 ≤ x ≤ ?/6

A:

Q: 5. Find the length of the curve given by x = cos t +t sin t, y = sin t – t cost, -T <t <

A:

Q: Find the slope of the tangent line to the parametric curves x=3t+2, y= 2t^2+ 3t-3 at t=11 and then…

A: The given question as belonging to the derivative in which we have to find the derivative or the…

Q: What is the equation of line tangent to sin r+1 y = at the point (T, -1)? cos E O y= TX –1 - O y = 1…

A:

Q: 10. Find the exact length of the curve y = In(sec x),0 < x<T/4 %3D

A: This is a problem related to integration of the function. Based on the integral formula we will find…

Q: The Tschirnhausen cubic is the curve given by the equation x^2=y^3+3y^2 At which point(s)…

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Q: Find the lengths of the curves x = ln (sec t + tan t) - sin t , y = cos t, 0 … t … pi/3

A: x=lnsect+tant-sint,  y=cost,  0≤t≤π3 Differentiating with respect to t, we get ⇒dxdt=1sect+tantsect…

Q: 5. Find the length of the curve given by y= Vt* – 1 dt and 1<x<2.

A:

Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = cos t, y = tan t

A: Given that, x=cost, y=tant We have to eliminate the t and express curve in the form y=f(x). As we…

Q: 7. Find the slope of the tangent to the parametric curve x = t - lnt, y = t + lnt at the point (e +…

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Q: Find the length of the curve x=cos^2t, y=sin^2t, 0≤t≤Pi.

A: In this question,we find the arc length of the curve using x=cos^2(t),y=sin^2(t),0&lt;=t&lt;=pi Arc…

Q: Q4: Find an equation for the line tangent to the curve 2y cos x = 4x sin y , at the point where x =…

A:

Q: 1. Make the curve y = ax°+ bx² +cx +d through (0,3) and have at (1, 2) a point of inflection with a…

A: To make the curve.

Q: 2. Find the length of the curve r(t) = e'i + e' sin 2tj + e' cos 2tk, 0st< 2n.

A:

Q: The extremum for the variational problem:- SLy + 2yy'-16y"Jdx; y (0)-0; v =1 occurs for the curve…

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Q: 8. Find the length of the curve defined by x = cos(2t), y = sin(2t) from t = 0 to t = n.

A: If x = f(t), y = g(t) in (a, b) then length of the curve is,

Q: The slope of the tangent line to the curve parametrized by the equations x (t) = -2(cos(t) + t…

A: Slope of tangent is equal to dy/dx.

Q: (11) Find the tangent line(s) to the parametric curve given by * = t5 - 4t3 y = t2 at (0, 4)

A:

Q: (a) Find the equation of the tangent line to the curve x = e', y=e %3D at t = 1 without eliminating…

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Q: Find equations for the a) tangent line and b) normal plane to the curve 1 x=t- cost, y = 3+ sin 2t,…

A: x=t-cost, y=3+sin2t, z=1+cos3t We know that rt=xt, yt, zt dxdt=1+sint, dydt=2cos2t, dzdt=-3sin3t At…

Q: Find parametric equations for the tangent line to the curve given by x=ln(t+1), y=tcos2t, z=et at…

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

A:

Q: 1. Find the equation of the tangent plane to the surface cosh [exp (x²y)] = Z y? at the point where…

A: We will find out the required equation of tangent plane.

Q: Find the exact length of the curve. x = 9 cos(t) − cos(9t), y = 9 sin(t) − sin(9t), 0 ≤ t ≤ pi

A:

Q: (a) Find the slope of the line tangent to the curve y = sin x at the point where x = T/3. (b) Show…

A: (a) we have to  find the slope of the tangent line to the curve y=sin5x at the point where x=π3. as…

Q: Find the exact length of the curve. y = (x-x2)1/2 + sin-1((x1/2))

A: The arc length formula is given as

Q: Find the slope of the tangent line to the curve y = g²+4r+7 at the point (0, 3). 7a+2 Determine da…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: eliminate the parameter to find a cartesian equation of the curve x= sinh(t),  y= cosh(t)

A: x=sinht,  y=cosht

Q: Use the method of isoclines to draw several solution curves for the equation: dy/dx = x/y

A: We can use isocline lines to draw constant slopes along that line. Using some (at least four but six…

Q: At what value of x does the curve 1„2 sin y = 3y +x² + 4x have a horizontal tangent? (Supporting…

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Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A: