find the terminal point P(x,y) on the unit circle determined by the given value of t t=pi/6 P(x,y)=(        )

Q: Find the tangent line to the Curve t) =(sin 4), cos (t),+> at (0,l,0) क

A: We are given parameteric equation of curve .

Q: Find the arc length of the graph of the function over the indicated interval. x = (1)/(3)(y2 +…

A: Given x=13y2+232 ,0 ≤ y ≤ 8.

Q: Find the arc length of the graph of the function over the indicated interval. 3/2 + 1 2 y = x2 3 y 4…

A:

Q: Find the length of the curve using formula.  y= ln (cosx) bounded by 0 and pi/4

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Q: (a) Find the arc length of the curve y = (4 – x3 over the interval [0, 8].

A: " Since you have asked multiple question, we will solve first question for you. If you want any…

Q: 4. Find the length of arc of the curve x3 + y3 = 1 in the first quadrant from the point where x = to…

A: If a function f(x) is defined over an interval [a,b], then the formula for arc length is: Formulae…

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 plane to the surface at the given point. g(x, y) = arctan L, , (3,…

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Q: Find the arc length of the graph of the function over the indicated interval. 3/2 2 x + 1 3. y =

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Q: Find the length of the curve. x = cos t y = sin t

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Q: Find the arc length in the second quadrant of the curve x23 +y2/3 = 25 from x = - 125 to x = – 8.…

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Q: Find the length of the arc of the curve y =: +e*) from x = 0 to x =2.

A: y=ex+e-x2

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

A:

Q: Find an equation for the line tangent to the curve x= 2sin(t), y= 4cos(t) at the point defined by…

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

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Q: Зп 2. Find the exact length of curve y = ln (cosx), * < x < n. 4

A:

Q: Find the point(s) on the graph of y = (x2 – 168)e × where the tangent line is horizontal. Identify…

A: Given y=x2-168ex Consider, fx=x2-168ex To find the points on the graph where the tangent line is…

Q: Find the arc length of the graph of the function over the indicated interval. x2 3/2 + 1 y = y 4 1 3…

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Q: (b) The tangent plane to the graph of z = f (x, y) at the point (1, 0, 1) can be described the…

A: We need to find the tangent plane to the graph of f(x,y)=e3yx4 at the point (1,0,1)

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: Find the arc length of the graph of the function y = ln(1 − x2 ) on the interval 0 ≤ x ≤ 1/2

A: Given:            y= ln 1-x2,  0≤x≤12    Formula to be used: Let y=f(x) be differentiable function…

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

A:

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: Find the slope of the tangent line to the path of a carnival ridex=8 cos(t) + sin(81), y = 8 sin(t)…

A: The slope of the tangent is dydx.

Q: Find the length of arc of the curve 6xy = x^4 + 3, from the point where x=1 to the point where x=2

A: The given curve is: 6xy=x4+3 y=x46x+36xy=x36+12x Differentiate it: dydx=3x26-12x2dydx=x22-12x2

Q: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l

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Q: Find the point on the cycloid c(t) = (t − sin t, 1 − cos t) where the tangent line has slope 1/2.

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Q: Let P(cosh t, sinh t) be a point on the unit hyperbola x2 − y2 = 1 in the first quadrant . Show that…

A: Redraw the given figure as shown below.

Q: Find the exact length of the curve. y = 6 + cosh(3x), 0s x 8 중이nh(3) sinh(3)

A:

Q: Find the exact length of the curve. y = ln(cos x),   0≤ x ≤ π/3

A: Formula used: L=∫ab1+dydx2dx

Q: Find the length of the arc of the curve y = ln x over the interval: 1, 7| . Round the answer to four…

A:

Q: Find the length of the curve y = ln (cos x), 0&lt;= x&lt;= pai/3

A:

Q: 22. Find an equation of the tangent line to the curve at a given point y = e* cos(x), (0, 1)

A: Given:      Curve y=ex cosx     point =0,1   Finding slope m of the tangent evaluating the…

Q: Find any points on the curve given by I =t+ sin t, y = cos (t), 0 <t< 2n where the tangent is (i)…

A: The given problem is to find the points on the given parametric curve where the tangent is…

Q: V. The tangent line at the point (t, y) = (- to 4'2 1 Then, the curve y = cos t is y = bt - - - a a…

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Q: Find the length of one arch of the cycloid = 5(t-sin(t)),y- 5(1-cos(t)).

A:

Q: Find the lengths of the curves x = cos t, y = t + sin t, 0≤ t ≤ π

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Q: 8. Find a parameterization of the tangent line to r(t) = (cos(t), sin(2t)) at the point

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Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: Given : x = cos2ty = cos t0 ≤ t ≤ 4π

Q: x = sin´t, y = cosʻt, 0<t<3™

A: Given x=sin2t, y=cos2t, 0≤t≤3π

Q: Find the arc length of the graph of the function over the indicated interval. 3/2 x2 + 1 y = y

A: Here we need to find arc length of y from x=0 to x=1

Q: Find an interval of t-values with t > 0 such that c(t) = (cos t, sin t) traces the upper half of the…

A: Given,  ct = cost, sint  and t ≥ 0 We have to find the interval of t-values such that ct = cost,…

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Given,         x=t-sint , y=1-3cost , t=π3

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

A:

Q: Find the exact length of the curve. y = √(x - x2) + Sin-1 √x

A: Given curve is y=x-x2+sin-1x.

Q: Find the length of one arch of the cycloid x= 6(t-sin(t)) y= 6(1-cos(t))

A:

Q: Find any points on the curve given by x = t + sin t, y = cos^2(t), 0 ≤ t < 2π where the tangent is…

A: Here, the given curve is: x=t+sin t, y=cos2t, 0≤t≤2π To find the points where the tangent is…

Q: Find the values of x between 0 and π where the tangent line to the graph of y=sin⁡(x)cos⁡(x) is…

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