ind the equation for the tangent lin to y- fcx) at the specified point. fcx) where x=1 x2

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 points on the cardioid r = 1−cosθ at which there is a horizontal tangent line, a vertical…

A: Consider the given: r=1−cosθWrite the cartesian…

Q: The parametric form of the tangent line to the image of f(t) = (2t², ?,t +2) at t = 1 is L(t) =

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Q: Find the equation of the tangent plane to the graph of G(u, w) = sin (uw) at the point (r, ).

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Q: Find the length of the curve r = cos(f) + sin(0), 0sOs

A: The objective is to find the length of the curve.

Q: The slope of the tangent line to the graph of y I cot I at x = 1 is Coloot ono:

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Q: Find the tangent of KJ. E H G tan (J)

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Q: Find the length of the curve over the given interval. r = 1 + sin θ, [0, 2π]

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Q: There is only one point with a horizontal tangent line to the graph of the curve y = x + cos x in…

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Q: ind the equation of the tangent line to the graph of f(x)= 3e* +1 where x, = In 2.

A: Slope of tangent line is (m) given by derivative of curve at given point. Let the curve be f(x) and…

Q: Find the length of the curve over the given interval. r = 4 sin θ, [0, π]

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

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Q: Find the points on (t + sin t, t − 2 sin t) where the tangent is vertical or horizontal

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Q: ind the length of the curve x cos(t) + In(tan(;t)), y = sin(t), /4<t< 3n/4. %3D ength =

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Q: Find the equation of the tangent line to the given function at z = a. w(2) = tan (3x) +x, a=0 3 !!

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Q: e) With respect to y = cosx, is there a vertical stretch or compression? f) With respect to y =…

A: To answer parts e and f

Q: Find the exact length of the curve. x = 7 cos(t) – cos(7t), y = 7 sin(t) – sin(7t),

A: given : formula for arc length is as below :

Q: Find the speed of the cycloid c(t) = (2t – 2 sin t, 2 – 2 cos t) at points where the tangent line is…

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Q: Let (a, b) be an arbitrary point on the graph of y = 1/x, x &gt; 0. Prove that the area of the…

A: The given function for the curve is, y=1x The slope (m) of the tangent at the curve is,…

Q: Find an interval of t-values such that c(t) = (cost,sin t) tracesthe lower half of the unit circle.

A: Consider the given point as ct=cost,sint

Q: Find the slo pe of the Para bola y=X at the Point PC2,4).write an equation for the tangent to the…

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Q: ind the equation of the tangent line to y = f(g(x)) at x = 1. %3D

A: We have given two graphs of two functions f(x) ,g(x). We have to find the equation of the tangent…

Q: Find the slope of the tangent line to the trochoid x = rt – d sin(t), y=r – dcos(t) in terms of t,…

A: Given: x=rt-dsin(t), y=r-dcost To find: Slope of tangent line to given trochoid in terms of t, r and…

Q: ind the tangent line for the following 3. x3 + y3 – 6xy = 1 at (2, 3) 4. (x² + y²)? = 4x²y at (1, 1)

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Q: The slope of the tangent line to the graph of y? = In(ry) at the polnt (e, 1) Is Select one: a.e=1…

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Q: Find the equation of the tangent line (assuming it exists) to f(x) = x² + x at x = -2. Give your…

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Q: A satellite (S) in orbit around the Earth is sending two signals that are tangent to Earth at points…

A: Given that , mACB⏜=208° mAB⏜=152° ∠S=?

Q: Find the points on the cardioid r = 4(1 – sin0) at which there is a horizontal tangent line, a…

A: According to the given information, it is required to determine the horizontal tangent line,…

Q: Find the equation of the tangent to the curv e y = 23 Az-12 at the point where a = 3. Answer:

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Q: Calculate the length of the curve r=a*sin(^3)(x/3) for (x(1)=0, x(2)=3pi)

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Q: Find the equation of the tangent line to y= sech? (x) . = In(3). at x

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Q: Prove that all normal to the curve x =acid+at sin t, Y=a sin t-atcost.Are at a distance a from the…

A: We need to prove that normal to the given curve are at a distance of a from origin.

Q: The equation of the tangent line to the graph of VT is given by y = mx + b for y = tan(4x) at x = т…

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Q: 9. At what point(s) on the circle x 2 + y? = 13 is its tangent line parallel to the line 3x – 2y = 6

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Q: ind all the tangents to the curve y cos (x %3D

A: Here we have to find the tangents on the curve y=cos(x+y)...........(1)     , -2π≤x≤2π parallel to…

Q: e, Find at the giren point on eauation Of the tangent live. to the corve. X=46",y=f'+|,(4,0)

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Q: Find the exact length of the curve. y = 2 In(cos (÷)) Tt/3 < x <T/2

A: Here given Differentiate the given function with respect to x using the chain rule of derivative

Q: Find an equation of the tangent line at the point specified.

A: Consider the given equation as And

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

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Q: Find an equation for the tangent line to the curve parametrized by x = e³t sin(πt) and y = et at the…

A: x=e3tsin πty=e2t

Q: . Find the slope of the tangent line to sin(z – x) + y° cos.x = y at( А. 4 В. -1 С. О D.

A: This is the final solution of given question.

Q: Determine the equation of the tangent line to (a) r = 2 sinθ at θ =π/6 (b) r =1 + cosθ at θ =π/2

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Q: The parametric form of the tangent line to the image of f(f) = (4i², 2,t – 3) at t = 2 is L(t) =

A: To find the parametric form of the tangent line to the image of f(t)

Q: Find an equation of the tangent line to the curve f(r) = sec2 x + tan? r at I = T/4.

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Q: The parametric form of the tangent line to the image of f(t) = (3t2,,t – 2) at t = 2 is L(t) =

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Q: Find the arclength of the curve over the given interval. (a) r = 1+ sin 0, 0 <o < 27

A: Solution is given below:

Q: 23. Find (to two decimal places) the coordinates of the point P in Figure 9 where the tangent line…

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

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Q: ind an equation of the tungent line to y= 45in2 X at point (i II

A: