the sloper of the curve 2y = ax? +b at (1,–1) is – 1.Find a, b

Q: Find the exact length of the curve. x- 2, y=? - 2, Osts 6

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Q: (b) Investigate where the curve y = xy4 - x² is concave up and concave down?

A: Given curve is y=x4-x2 find the concavity of the given curve

Q: Find the length of the curve y = xVa 0 <x < 1.

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Q: Find the exact length of the curve. x = et - 4t, y = 8et/2, 0≤t≤2

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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…

A: Given

Q: = V4 cos" : – 1, y = 10 < x < 30

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Q: Find the equation of y, glven the derlvative and the Indicated polnt on the curve. dy = 2x- 1 xp

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Q: Find the exact length of the curve. = 플Vy (y-3), 4sys 16 3

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Q: Find the points on the curve æ = t² – 6t – 8, y = t² + 14t – 6 that have: A. a horizontal tangent…

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Q: Evaluate [(x +2y) ds, where C is the curve defined by y = √√4 – æ², for x = [0, 1

A: Here ds is arc length.

Q: The x coordinate of the point of intersection between the two curves y = el4a and y = 1 is

A: Equate both equation

Q: Find the exact length of the curve. y - 4 + 2x 3/2, o sxS1 1.547

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: Find the exact length of the curve. x = et − 9t,    y = 12et/2,    0 ≤ t ≤ 2

A: Note that:Arc length formula = ∫abdxdt2+dxdt2 dt                   where , a≤t≤b       Given,…

Q: For what values of a and b is the line 5x + y b tangent to the curve y ax³ when x = 2? a = b

A: Given curve , y=ax3-1 at x=2and given line 5x+y=6-iiwe have to find the values of a and b such…

Q: Find the exact length of the curve. =글Vy (y-3), 16 <y< 25 X =

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Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t at t = 0.…

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Q: Find the equations of the tangent lines x = t3 − 6t, y = t2 at the point where the curve crosses…

A: To find the equations of the tangent linesx=t3-6t,y=t2 at the point where the curve crosses itself.…

Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangents to the curve at x=2…

A: Solution is here

Q: 1) Given the curve 2x? + y3 = x3 + y? find the x-intercept of the tangent line at the point (2,1)

A: We find dy/dx using the implicit differentiation and we plug x=2 and y=1

Q: Find the exact length of the curve. Vy (y - 3), 16 < y < 25 X =

A:

Q: Find the values of a and b for the curve x2y + ay? = b if the point (1,1) is on its graph and the…

A: The slope of the tangent 'm' at a point (x1,y1) for a curve S(x,y) Is given by dydxx1,y1 therefore…

Q: If a curve C is given by r(t) = ⟨t, t2⟩ , what is | r'(t) | ?

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Q: Sketch the two curves 7(t) = tî + t²j; t e [1, 5] and B(T) = e"î + e²r3; T E [0, In 5]. How are they…

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Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangent to the curve at x=2…

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Q: Find the length of the curve given by x(t) = 1 + 3t² ,y(t) = 4 + 2t³, 0 <t < 1.

A: xt=1+3t2yt=4+2t3 Differentiate the above equation w.r.t."t"…

Q: Find the length of the curve. r(t) = (4t, 0 <ts 1

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Q: Find the slope and concavity of the curves at the given points. r = eθ, θ = 0, π

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Q: Show that the equation of the tangent to the curve = 2 (a'0, b1.0) a y at the point (a, b) is = 2.…

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Q: The family of curves orthogonal to x2 + 4y2 = c2 has the general equation 04. %3D

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Q: a) Given a curve y = px* + 2x has turning point at (–1,q). Find the value of p and q.

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Q: y = e*, 0<z<1.

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Q: Find the exact length of the curve. y = In(sec(x)), OsxSa/4

A: Length of a curve f(x) in interval [a,b] is given by ∫ab1+(f'(x))2dx

Q: Find the equations of the tangent lines x = t2 − t, y = t3 − 3t − 1 at the point where the curve…

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Q: Find the path of the sloping path y = x² + c such that θ = π / 4 is the angle between the tangents…

A: Slope = 1  Point are (a,b) So equation of tangent      Y-b = 1.(x-a)

Q: Find the length of one branch of the curve ay? = x3 from x = 0 and x = 5a. 4.

A:

Q: Evaluate ∫C x ds, where C is the parabolic curve x = t, y = t2, from (0, 0) to (2, 4).

A: Given: Parabolic curve x=t, y=t2 from (0,0) to (2,4)

Q: Find the points on the curve t2 – 14t – 1, y = t² + 6t + 5 that have: х — A. a horizontal tangent…

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Q: Find the length of the curve r(t) = (1,t2, t³). 0<t < 1.

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Q: Find the length of the curve r= e2θ, 0≤θ≤2

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Q: Evaluate (2 - xy) ds where C is the curve given below. -2 -1 -2

A: Given   ∫C2-xyds Curve C

Q: Find the length of the curve. 6t, , r(t) 0 <t< 1

A: Given:-r(t)=6t, t2, 19t3,         0≤t≤1since we have to find the length of curve.

Q: Find the exact length of the curve. x = et + e=t, y = 5 – 2t, 0st< 4

A: The solution are next step

Q: Express the curve by an equation in a and y given #(t) = t² and y(t) = 2 t4 + 6. а) x = 4 y? + 5, y…

A: To convert the parametric equation into cartesian we must have to eliminate parameter t from both…

Q: Consider the implicitly defined curve xy? +3x2 = 4. %3D Verify that the point (1, 1) is on the…

A: Consider the following curve: xy2+3x2=4 Substitute x=1 and y=1 in the above curve:…

Q: For the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A: We have to find the value of a and b according to the given information

Q: Find the exact length of the curve. 36y? = (x2 – 4)3, 5< xs 6,

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Q: b) Find the points on the curve 2 17x + 12xy + 8y“ = 100| that are farthest away from the origin…

A: Substitute x = rcosθ and y= rsinθ

Q: For the curve y= ax + bx? + 12x - 7, what values of a and b will make the tangents to the curve at…

A: