Show that the square of the length of the subtangent at any point on the curve by2=(x+a)3 (b is not equal to 0) varies with the length of the subnormal at that point

Q: Show that the square of the length of subtangent at any point on the curve by2=(x+a)2 (b is not…

A: Here given curve  by2=x+a2

Q: show that the square of the length of subtangent at any point on the curve by2=(x+a)3(b is not equal…

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Q: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

Q: The tangent line to y=f(x) at (2/(2) is line through given point whose slope is equal to (a) f (a)…

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Q: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

Q: mine an equatio

A: Here we have to find the equation of rectifying plane to We have,

Q: Find the tangent line to g (x) 16 4T at z = 4.

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Q: Find the slope of the tangent line to the curve of intersection of the graph of z = 2x2 + 3xy + 2y2…

A: We need to find slope of the tangent line.

Q: Find the length of the curve y 2ln(x) from x 1 to x =4. %3D

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Q: What is the area of the triangle bounded by the x and y axes and the tangent to the curve xy^2=4 at…

A: xy2=4 Differentiating with respect to x, we get…

Q: Find the arclength of y = 2x2/3 from x is greater than or equal to 1 and less than or equal to 2

A: The arc length of the function y=2x23 between x=1 to x=2.

Q: find the point on the line y=2x+10 that is closest to the orgin, (0,0) What is the minimum distance?

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Q: Find the exact length of the curve given by Length = x = 2t², y = (0 ≤ t ≤ 4).

A: A detailed solution is given below

Q: The tangent line to the curve il me f(a) at 2 m 1 goes through the points y=f(x) x == and Find the…

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Q: 2. Find the slope of the tangent in the positive x-direction and y-direction to the surface z = 2xy…

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Q: 13. Show that the length of the portion of any tangent line to the ball x2/3 + y2/3 cut off by the…

A: Given: The equation of the ball is: x23+y23=a23...........(1) We have to show that the length of the…

Q: Find the slope of the tangent in the positive y-direction to the surface  z = 3x + 2y − 4exy at (4,…

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Q: find the tangent line to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: Given the parabola x+2y2+2x-y-3=0..............i  Determine the slope of given line x-4y=2…

Q: Find the exact length of the curve over the given interval. 1 along 1 < y < 2. 8 4y2 ' ||

A: Find the length of the given curve

Q: Prove that the point of the tangent intercepted between the axes at any point on the curve x…

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Q: Find the slope of the tangents to the curve at the points (P1 and P2) where it crosses the x-axis.…

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Q: For a χ2-curve with 19 degrees of freedom, find the χ2-value that has area a. 0.025 to its right. b.…

A: a) Degrees of freedom is 19 The chi-square value that has area 0.025 to its right is given below:…

Q: 8how that the square of the leng point on the curve by = (x + a)° , length of the subnormal at that

A: Subnormal and Sub tangent: Allow y=f(x) to be the differentiable curve at point P. Let the tangent…

Q: show that the sum of the x-intercept and y intercept of any tangent line to the curve x1/2+…

A: Consider the given equation of curve, x+y=cddxx+y=ddxc12x+12ydydx=012ydydx=-12xdydx=-yx Therefore,…

Q: Find the slope of the tangent in the positive x-direction to the surface z = 3x3 - 7xy at the point…

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Q: Show that the square of the length of subtangent at any point on the curve by 2 = (x+a)3,(b is not…

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Q: gion shaded in light blue is bounded by two curves, y = (x – 1)? + 33 (in dark red) and z+ 3)² + 1…

A: We will find the area between the curves.

Q: The tangent plane to the graph of the function :==3y+1=(1+y} at the point (1; 1; 3/2) contains point…

A: The given equation of the surface is z=x2y+1. Rearranging the above equation gives, w=z-x2y-1 Find…

Q: Use Simpson’s Rule with n  =6  to estimate the length of the curve x  =t - et -6&lt;t&lt;6

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Q: Find the equation of the tangent line to f(x) = 8x² – 5x – 40 at (3,17). %3D

A: Solution of the problem as follows

Q: For what vaules of x in the interval [0,2π) does the fraph of g(x)= (√3)x+2sinx+7 have a horizontal…

A: For horizontal tangent,first derivative must be zero

Q: on of the tangent to y = 3e" + 3ex that is parallel to

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Q: Find the equation of the tangent line (assuming it exists) to f(x) = x² + x at x = -2. Give your…

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Q: The surface of a hill above the xy-plane is described implicitly by 3x² + y² + (z + 1)² = 2, z ≥ 0.…

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Q: Find the tangent line, in standard form, to y= f(x) at the indicated point. y = 4x2 – 5x + 8, at x=…

A: →Let y=f(x)    Slope, m =dydx→Equation of straight line passing through (xo,yo) with slope m is…

Q: The value of b makes the liney = 2x + b be tangent to the function f (x) = x² is

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Q: Find the length of the curve defined by the y-axis. over the interval <r< 1 about 2.r

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Q: दलालभ यला Find an equafion of the tangent line to the ceurve at the grven point. y=x3-3x + 1, (2,3)

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Q: Show that the square of the length of subtangent at any point on the curve by =(x+a)°.(b÷0) varies…

A: We will prove it as following.

Q: 2i Find the eguation of the tangent: lime to tul Cur ve y=4x -x* at the point (l,3).

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Q: . Evaluate the length of the curve, y = x/2, from x = 0 to x = 4. %3D

A: first step differentiate w.r.t to x

Q: find the points on the curve where the tangent is horizantal, X=t^2+1,y=3t^2+t

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Q: In the xy-plane, the line x + y = k, where k is a constant, is tangent to the graph of y = x^2 + 3x…

A: Given line is x + y = k, where k is a constant it is tangent to the graph of y = x^2 + 3x + 1…

Q: Consider the curve satisfying y" = 6x and is tangent to the line y = 5– 3x at x = 1. What is y' (2)?…

A: Given: y''=6xand tangent to the line y=5-3x at x=1To find y'(2)=?

Q: Find the point on the curve y=/2 for which the tangent ine to the curve is perpendicular to the line…

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Q: Find the points on the curve y = 2x3 + 3x2 − 12x + 9 where the tangent line is horizontal. a)…

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Q: Find the equation of the tangent plane to z=6x2+2y2  at the point (1,5)

A: Given  z = 6x2+2y2  at the point (1,5)

Q: What is the length of the -3< x S3 segment of the y = v36 – x2 www vwwb w e curve?

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Q: The slope of the tangent line to the graph of x + y + xy = 3 at (1, 1) is Blank 1.

A: Let's find.