4. Sketch the graph of the curve y = Vĩ and the tangent line in the Cartesian Plane using a scale of 1 unit = I cm. Show in your diagram the line segments dx, dy, and Ay, similar to Figure 4.5.1. [Note: the curve is an upper semi-parabola whose vertex is at

Q: 1 2 #5) A) Find the length of a curve y Inx for 3 < x < 7. 4

A: L= integration of sqrt of 1+ (dy/dx)2 dx from a to b

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A: Given: Parabola:y2=4xLine:x+y+4=0   A and B are the points of intersection of C with the line y=−5…

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Q: 3) Find the exact length of the curve: x = y = In(1+t); 0<t<2.

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Q: 1. Find the equation of the tangent plane to the given surface at the point (0,-1,-2). * 2r2 „2

A: by using formula of plane

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Q: 1. Consider the curve C given by y = 5 + 2x3/2, 0 < x <1. (a) Find the length of the curve C.

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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

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Q: 17. Calculation S,(x - y+ ix2) dz, where C is the curve form 0 to 1+i.

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Q: Consider the following. x = et − 4,    y = e2t   Eliminate the parameter to find a Cartesian…

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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: 1. Find the moving trihedral and the curvature at any point of the curve R(t) = cost î + sint j+k.

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Q: Find the equation of the tangent line to right branch of the hyperbola π π ㅠ x = sect, y = tant, st≤…

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Q: Problem 4: For what valnes of a and o s the line y=-2x+b tangent to the parabola y=Ox° whern X=2?

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Q: y = 1/2 (e² + e^¹), − 1 ≤ x ≤1

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Q: 2 4. Find the length of arc of the curve x3 + y3 = 1 in the first quadrant from the point where x =…

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Q: 7. Given that the line y = r -b is an asymptote to the ar curve y a,b €R,rz 1, then b = A -1-a 1-a C…

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Q: 1 1 from x=1 to x=3. 4x 3 5. Find the length of the curve given by y 3

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Q: (6) Find the points on the curve 5x2 + 6xy + 5y² = 9 which are nearest to and farthest from the…

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Q: A curve C is given parametrically by x = cos(t) - 2 and y = sin(t) + 3, where 0 ≤t≤ 2π Find and…

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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: Two stations, located at M(1.5, 0) and N(1.5, 0) (units are in km), simultaneously send sound…

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Q: Below is a plot of a cardioid, which consists of points satisfying x² + y² = (2x² + 2y² - x)² 0.6…

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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: 12 1 If the curve shown in the figure is rotated about the y-axis, this creates the shape of a

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

A: Formula used: L=∫ab1+dydx2dx

Q: 7.) Find the shortest distance between (4,2) and the curve y? = 8x.

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Q: 1. Find the exact length of the curve. (a) y² = 4(x+ 4)°, 00 (b) y = In z, 1<I<2

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Q: 7. Find the exact length of the curve: x (t) = 2t, y(t) = 2t, 0 ≤ t ≤ 1

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Q: 2 Consider the two graphs y = 2x and x - xy + 2y = 28. The absolute value of the tangent of the…

A: Introduction :

Q: 3/2 The length of the curve x= 4y2 from y=1 to y= 4 is given by

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Q: 6.2 Finl the Voune of the Selid enclosed by the curves y=eX, y=0 x=0,'= "about the x-axs.

A: Given: y=ex, y=0, x=0, x=1 From the given curves the bounded region is as shown below; Apply the…

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Q: A curve is described parametrically as x = e' sint, y = e'cost, – o <t< ao. Find the equation of the…

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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 the exact length of the curve. 9 s ys 16

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Q: AT is tangent to oG. 8 10 Find: AN. AN = %3D units

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Q: Find the isogonal trajectory of the family of curves y + 2xy – x² = k where tan a = 1

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Q: 6- Which of the following is the shortest distance from the point (15, 0) to the curve y = V6x ? a)3…

A: Solution: The objective is to find the shortest distance from the point (15,0) to the curve y=6x

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

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Q: 3. Plot both the following curves on the same set of axes. r = 5 - 4 cos e and the parabola y = r.

A: Given

Q: Find the length of the arc of the curve x2=(y-2)3 from P(1,3) to Q(8,6).

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Q: Question 5 Find the length of the curve. +- from y = 1 to y = 2 %3D 4y2 2

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