1. Eliminate the pametric t to get an equation relating x+y. ldentify the graph of the resulting equation: U* X-2 = 5 sint i Y+ 1 = 3 cost

Q: Eliminate the parameter to find the Cartesian format, then sketch the graph: а. x = cost y = cos² t…

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Q: Show that the curve y = x? sin 3x touches the parabolas y = x andy =-x² alternately at infinite…

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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: Use the graph to approximate the number of points of intersection of the graphs of y1 and y2.

A: We are asked to find the solution of the graph

Q: 4. a) Find the entire are length of the curve r = 2a cos³ (0/3).

A: 4a Given curve is r=2acos3θ3. We have to the entire arc length of the given curve. The entire arc…

Q: 1 Find the exact length of the curve: r(t) = , 6.

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Q: Find the length of each of the following curves: %3D %3D x (ey + e) from y = 0 to y = 1

A: The length of a curve means the arc of the length of a curve. The arc of the length of a curve in…

Q: Sketch a graph of I = t + 2t, y = t +2, t > –1 . %3D

A: Given equations are x=t2+2t,y=t+2,t≥-1. So list the values of t and obtain the coordinates in…

Q: 3. Deduce from the orbit equation (1 + e)ro 1 + e cos 0 that a planet is closest to its sun when 0 =…

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Q: Find the arclength of y = 4x - 2 on 0 < x < 1

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Q: 23. CAS Find a good numerical approximation to the coordinates of the point on the graph of y = In…

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Q: Ex(4) A particle moves from point (-2,5) to y-axis in such a way that Ay = 3Ax. Find its new…

A: Solution is given below:

Q: 2. 6. 2. (3), 6. (x) 10. 12- 14. (4, 17) 16. B. 18+ f4)= 2x2+1 Find the arc length of the graph from…

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Q: Q3 Find dyldx on the graph y secx + y = cos2x at point (1, 2).

A: We have to find the derivative of above function at (1,2) Please see the explanation below

Q: 10. Which of the following is the tangent line equation of the ellipse 9(x +y)² + (x – y)² = 36 at…

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Q: Find the arclength of y = 3r/2 on 1 < a < 3

A: As we know that the expression for the arclength is:   l=∫x1x21+dydx2dx...(1)   Given: y=3x32x→1 to…

Q: •x= 5+4 sin 0 and y = -3 + 2 cos 0

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Q: Find the arclength of y = 2a + 4 on 0 < a < 4

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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: Sketch the graph of y = m(r) in Figure 2. %3D 음-3, rS-1 m(x) = 4 %3D 1<r<5

A: Given,          mx=13x-3x≤-141&lt;x&lt;5

Q: 11. dy/dx = -x/y, y(0) = 4 %3D

A: Given: Let's sketch the isoclines and their direction markers, then sketch a few solution curves,…

Q: ind the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -1,…

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Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: Find the arclength of y = 2x/2 on 1 < x < 3

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Q: 13. dy/dx = 2x, У (0) 3D —1

A: Solution: dy/dx =2x  ,    y(0)=-1

Q: Sketch a graph for y = 2 sin (x+=) + 1, x E [0, 4n] (show full working out for all intercepts and…

A: The function is y=2sinx+π3 +1, x∈[0,4π] Obtain the y-intercept: Set x= 0, y=2sinπ3 +1≈2.732; Obtain…

Q: The Gateway Arch in St. Louis was designed by Eero Saarinen and was constructed using the equation…

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Q: 2. Find the point on the curve y = VI thats is closest to the point (3,0)

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Q: 7- Find the leng thof the Curve arce 34 from to y=4

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Q: 1. The graph of y--k is shown in the xy-plane above, where & is a constant. If the arca of APOR is…

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Q: 3. Find the angle or rotation and new equation of curve 9x2 + 24xy + 16y2 + 90x – 130y = O such that…

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Q: 1. Find the arclength of y= (4 -x3,3/2 from x = 1 to x = 8.

A: The arclength of given equation

Q: A particle travels along the parabola y = ax^2 + x + b. At what point do its abscissa and ordinate…

A: Given: y=ax2+x+b

Q: Show that the equation of the tangent line to the hyperbola x2/a2 − y2/b2 = 1 at (x0, y0) is x0x/a2…

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Q: Find the arclength of y = 4x + 3 on 0 < x < 2

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Q: A particle is moving on the curve defined parametrically by the system of equation x = 1- 2cos?t and…

A: Distance of particle from origin is:

Q: 4. Find the two values of a for which the line connecting the point (1, –1) to a point (a, a²) on…

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Q: 4. Consider the equation of the hyperbola given by x2 + 2xy – y² = 7. Find an equation of the…

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Q: 3x + xy? 2y + x?y dy dx

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Q: 1. Find the equation of the tangent lines to the ellipse x² + 4y = 8 perpendicular to the line x +…

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Q: Find the arclength of y = 2x/2 on 1< x < 3

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Q: What is the value of c such that the line y=2x+4 is tangent to the parabola y=cx^2.

A: Given that the line y=2x+4 is tangent to the parabola y=cx2. The derivative of y=cx2 is dydx=2cx.…

Q: Draw the isoclines with their direction markers and sketch several solution curves, including the…

A: According to the given information, it is required to draw the isoclines with direction makers and…

Q: Find the arclength of y = 2x/2 3/2 on 1 < x < 3

A: We know that the arclength of a curve y=f(x) on a≤x≤b is given by L = ∫ab1+f'(x)2 dx

Q: Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

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Q: Find the diffrential equation of for each of the curves determined by the condition that at each…

A: length of subtangent =ydydx

Q: Two different level curves of the graph of z = f(x, ygan intersect. O True False

A: The level curve of a function f of two variables are the curves with equations f(x ,y)= k, where k…

Q: 1 Find the stationary points and state the nature of the curve y=xe.

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