Show that the curve y =  √ (4x2 +9) has two slant asymptotes: y = 2xand y =-2x . Use this fact to help sketchthe curve.

Q: Find the length of the curve defined by Y = 3x³/2 + 3 from x :3 to x = 9.

A: Question: Find the length of the curve defined by y= 3x^3/2 + 3 From x=3 to x= 9

Q: Find the exact length of the curve. 0 < x < 6 %3D 3

A: Given:   To determine: Exact length  of the curve     Concept: Exact length of the curve y = f(x)…

Q: For the curve y = 3x³ + 9x² – 27x + Locate the possible point of inflection.

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Q: Find the length of the arc of the curve 9y? 4x3 from the origin to the point (3,2v3).

A: Here, the given curve is: 9y2=4x3⇒y2=4x39⇒y=23x32 Now, the length of the curve on [a,b] is given by:…

Q: What are the coordinates of the points in the graph of y? – x² + 6x – 13 = 0 in which the tangent…

A: y2-x2+6x-13=0 --------------(1) Differentiating with respect to x ddxy2-x2+6x-13=ddx(0)…

Q: Find the coordinates of all points on the curve x^2 -2y^2 = 5xy-33 where the curve has a horizontal…

A: x2-2y2=5xy-33 →(1)Horizontal tangent slope is 0Differentiate (1) w.r.t…

Q: Does the curve y = x4 - 2x2 + 2 have any horizontal tangents? If so, where?

A: Consider the given function y=x4-2x2+2.

Q: Find the length of the curve y x² Inx 8 at (2 <x< 4)? -

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Q: Find the exact length of the curve.

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Q: The horizontal asymptotes of the curve 3x y = (x4 + 1)'/4 are given by %3D Y1 = and Y2 = where y1 >…

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Q: Describe the curve generated by x = 3 + 2t, y = -12 - 6t, for - ∞ &lt; t &lt; ∞.

A: Given: x=3+2t y=-12-6t            - ∞ &lt; t &lt; ∞ To find: curve generated by given functions.

Q: Find the equation of the tangent to the curve y= 3x' – 4x² +2x–10 at the points where the curve cuts…

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Q: Find the exact length of the curve. y 1x²-1-In(x), = 4 2 1 ≤ x ≤ 8

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Q: Find the exact length of the curve. y = 4 + 4x3/2, osxS1

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Q: Find the exact length of the curve. y = 4 + 8x3/2, Osxs1

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Q: Sketch the curve if y' is negative and y'' is negative on the interval of (-infinity, -3) with a…

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Q: Find the equation of the hyper bola with latus rectum 1, slope of asymptotes +- 1/2. Draw the curve.

A: Consider the general form of the hyperbola is, x2a2-y2b2=1 Since, the latus rectum is 1 then,…

Q: Find the exact length of the curve. y = 5 + 8x3/2, osxs1

A: Given: y=5+8x32,   0≤x≤1

Q: Use a graph to estimate the coordinates of the lowest point on the curve x = t³ - 31, y = 1² +1+1.…

A: Consider the parametric equation x=t3-3ty=t2+t+1 Sketch of the parametric equations is shown below.

Q: Show that the curve y =(1 + x)/(1 + x2) has threepoints of inflection and they all lie on one…

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Q: Find the exact length of the curve. 1 y = 4 -x² - In(x), 1< x < 8 2

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Q: Find the length of the arc of the curve 4y2 = 9x3 from the origin to the point (2,3v2).

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

A: we have to solve the problem

Q: Find the asymptotes of the curve y3+x2y+2xy2-y+1=0.

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Q: What is the length of the curve y = sqrt(4-x2) from x = -2 to x = 1?

A: y=4-x2 Differentiating with respect to x, we get dydx=124-x2·d4-x2dx   ∵dxdx=12x=124-x2·0-2x=-x4-x2

Q: How can we find the horizontal and vertical asymptotes of the curve?

A: We find the horizontal and vertical asymptotes of the curve

Q: Find the exact length of the curve. 2. y = 3 x3/2 Osxs1

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Q: Find the exact length of the curve. 는x - - In(x), 1<x<6 4 2

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Q: Find the exact length of the curve.   y = 1+ 6x3/2 , 0 ≤ x ≤ 1

A: Find the exact length of the curve.

Q: sketch the curve by finding the domain, intercepts, symmetry, asymptote, intervals of decrease and…

A: 1.) Find domain of the function:

Q: Use the guidelines of this section to sketch the curve. х — 6 y = x2

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

A: given  y=ax3+bx2+12x-7a=?b=?

Q: Use the guidelines of this section to sketch the curve.   y= 3√(x2  -1)

A: We need to find the x intercept, y intercept, vertical asymptotes, horizontal asymptote etc to…

Q: Find the exact length of the curve. y = 4 + 4x3/2, oSxS1

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Q: Use the guidelines of this section to sketch the curve.   y = 1/ x2 -9

A: Let us plot a table with values of x and y. x y 0 -8 1 -8 -1 -10 2 8.75

Q: Determine the points where the curve f(x) = 2x3 + 3x2 – 36x + 1 has a horizontal tangent. -

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Q: Find the horizontal and vertical asymptotes of the curve. 2ex y = ex – 6

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Q: Find the exact length of this curve : to y= 16 2x² |<x<2

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

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Q: Find the length of the curve y = x - lnx ; 1≤ x ≤ 4.

A: Given curve y=x-lnx  On closed interval [1,4] Length of the curve L=? Step 1 Find the derivate of…

Q: Find the exact length of the curve. 1 y = + 10x37 6 1 ≤ x ≤ 3

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Q: Find the exact length of the curve. x3 y = 1 < x < 2 %3D 4x

A: y=x33+14x  ,  1≤x≤2.

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

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Q: Find all points on the semicircle, y=sqrt 7-x^2, at which the slope of the tangent line is equal to…

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Q: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

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Q: Find the length of the arc of the curve 9y? = 4x3 from the origin to the point (3,2V3).

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Q: find the slope of the curve at the point indicated. 19. у %3D 5x — Зх?, X =

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Q: Use the methods of this section to sketch the curvey =  x3  -3a2x +2a3, where is a positive…

A: The curve is  y =  x3  -3a2x +2a3, where is a positive constant.

Q: The horizontal asymptotes of the curve 12x y = (zª + 1)'/ are given by Y1 = and Y2 = where yı > Y2-

A: Asymptotes are the tangents where the function tends to meet at the extremities of the x and y axes

Q: Find all asymptotes of the curve x2 + 3xy + 2y2 + 3x – 2y + 1 = 0 ?

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.