Q: Find the equati on of the tangent and normal to the following curves at the points indicated against. i) x = cos t, y = sin t at t = 4

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: i Find the eguation iof the tangent line to Uthe curve y sin 2x =X COS24 at Hohe point (T7/2,…

A: Explanation of the answer is as follows

Q: Q: Find the equati on of the tangent and normal to the following curves at the points indicated…

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Q: Q: Find the equati on of the tangent and normal to the following curves at the points indicated…

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

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Q: Q: Find the equati on of the tangent and normal to the following curves. at the points indi cated…

A: Firstly, find the value of the x and y coordinates, that corresponds to the given…

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 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 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 an equalion of the tangent line to the curve at the given point. y= (1+x) cos x, Co, 1)

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Q: Q: Find the equati on of the tangent and normal to the following curves at the points indi cated…

A: We have to find the equation of tangent and normal to the curves at the indicated point.…

Q: 2. Find equation of the tangent line at the point P given by t = where x(t) = cos (t) %3D y(t) =…

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Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

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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: Prove that the segment of the normal to the curve x = 2a sin t+a sint cos't, y =-a cos°t contained…

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Q: Prove that the segment of the normal to the curve x = 2a sin t+a sint cos't, y = -a cos't contained…

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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: 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: In this question we have to prove all normal curve are at distance 'a' from the origin.

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: Prove that the segment of the normal to the curve x = 2a sint+asint cos't, y = -a cos't contained…

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Q: A curve is defined by y=(1/3)sin(2x+1). Evaluate the angle between the tangent to the curve at x=2,…

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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: 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: Q: Find the equati on of the tangent and normal to the following curves at the points indi cated…

A: Solution

Q: 4. Find the slope of the tangent line to r = cos 0 at 0 = 3 %3D

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Q: Prove that the segment of the normal to the curve x = 2a sint +a sint cos’t, y = -a cos°t contained…

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Q: Prove that the segment of the normal to the curve x = 2a sint +a sint cos't, y = -a cos't contained…

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Q: Prove that the segment of the normal to the curve x = 2a sint +a sint cos't, y = -a cos't contained…

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Q: Prove that the segment of the normal to the curve x = 2a sint+a sint cos't, y =-a cos°t contained…

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Q: Prove that the segment of the normal to the curve x = 2a sint +a sint cos't, y = -a cos't contained…

A: First find derivative then equation of normal line ,and point of coordinate axes and then use…

Q: Prove that the segment of the normal to the curve x = 2a sint +a sint cos't, y = -a cos't contained…

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Q: Prove that the segment of the normal to the curve x = 2a sint+a sint cos't, y = -a cos't contained…

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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: find the tangent line of the curve (1– sin(1).tcos(1)) at the vale t(0) = T, (and so at the point(…

A: The curve is defined by the equations: x(t)=(t-sin(t))    and    y(t)=tcos(t)

Q: The slope of the tangent line to the graph of y = In(ry) at the point (e, 1) is .2 Select one: a.-e…

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Q: a) Show that the length of the arc of the curve y=f(x) where S(x) = Insecx 0SxS is 4 In(1+ v2)

A: We need to show that the length of the arc of the curve y=f(x) where f(x)=ln(sec(x)), 0≤x≤π4. The…

Q: Q: Find the equati on of the tangent and nomal to the following curves at the points indi cated…

A: →Slpoe, dydx = dydtdxdt→Equation of straight line passing through x1 ,y1 with slope 'm' is given by,…

Q: Find the length of the curve x(t) ešt cos(t), y = et sin(t) for 0 <t < 10. Give an exact answer,…

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Q: 61. Find the lines that are tangent and normal to the curve y = 2 tan( 7x/4) at x = 1. . %3D TTX

A: The given curve is  y = 2.tan(πx/4) Thr given point x = 1 At x = 1, y = 2*tan(π/4) y = 2 Point is =…

Q: what is the length of the curve y=1-cos(x) from x=0 to x=4pi

A: The given curve is  y = 1 - cosx dydx=0 - (-sinx)  =sinx

Q: Suppose L is the tangent line of f (x) = csc T at x = 2 . Where does L intersect the y-axis? Note:…

A: We have to find

Q: Find the points on the given curve where the tangent line is horizontal or vertical, where:…

A: Consider  the given information: Let  r=1-sin(θ)  ,0⩽θ⩽2π To find the points where the tangent line…

Q: What is the slope of the tangent line to cos(æ – y) = xe" at the point (0, ). O 1 -2 O None of these…

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Q: ) If y = cos2x + 2cosx for 0 < x < 2n. Find the points at which the tangent line is horizontal.

A: Given function is y=cos2x+2cosx for 0≤x≤2π. To find the points at which the tangent line is…

Q: Find the equation of the tangent plane to the graph of xe*y- eyz = In(x?) at the point (1,1).

A: Solution

Q: Find equations for the tangent and normal to the cissoid of Diocles y2(2 - x) = x3 at (1, 1).

A: Find dy/dx using the given equation.

Q: For the cardioid r  =1+ sin0 of Example 7, find the slope of the tangent line when  0=pi/ 3

A: Then plug this in the slope of the tangent formula

Q: Determine the equations of the tangent and normal at each of the points indicated. a) y = x2 + 3x +…

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Q: Find the length of the arc of the curve y=x+3 from the point where y=2 to the point where y=x^2+1…

A: y=x+3  ⇒x=y-3⇒dx=dy⇒dxdy=1 The formula for the length of the arc from the point y=2 to y=x2+1…

Q: Find the exact arc length of the curve over the stated interval. y = 7x2/3, from x = 1 to x = 8

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