6. Find the arclength of the curve y Note: L = 1+ (f'(x))² dx √ 1 x²+1 for -2 ≤ x ≤ 2.

Q: Analyze the graph of y = (arctan x)2.

A: Given- y=arctanx2 To Analyze- The above graph.

Q: x4 1 (a) Find the arc-length for y on the interval [1,4]. + 16 2x2

A: a) Find the arc length: y=x416+12x2on interval 1,4 Consider the given curve: y=x416+12x2Interval…

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

A:

Q: Compute the derivative of y = ln ( – V1 – 2 cosh x (x° + 2) |

A: To compute the derivative of,  y=ln1-2 cosh x .x3+2x.x-1.

Q: The figure shows the graphs of the functions y1 = x,    y2 = (1/2)x3/2 ,   y3 = (1/4)x2 , and y4 =…

A: The given functions are y1=x, y2=12x32, y3=14x2, and y4=18x52. We have to sketch the graph of the…

Q: x = 2 sin' (t) if 0<t< 2 sis Find the length of the curve \y=2cos² (t)

A:

Q: dy If y2=2x+3y dx find then use it to find the tangent line to the curve at the point (3,2) For the…

A: Solution is given below:

Q: Show that the inflection points of the curve y=sinxxy=sin⁡x/x lie on the curve y2(x4+4)=4.

A: Given: To prove that the inflection points of the curve y=sinx/x lie on the curve y2(x4+4)=4.

Q: The tangent line to the curve x'+y° -9xy=0 at the point (2,4) intersects the y-axis at y =. Write…

A:

Q: Find the sope to the tangent Iine of the equation ,-y +ear (0,3) Hirt perform impl cit…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Tangent are drown from the origin to the curve y = sin x.Prove that their points of contact lies on…

A: Consider the curve y=sinx Here, the objective is to prove that the point of contact of tangent from…

Q: Find the slope of the tangent line to the curve

A: Follow the procedure given below.

Q: For the curve r-y +2xy-y+1=0: a) Find the derivative dy/dx. b) Where do the horizontal tangent lines…

A: follow the next step

Q: The length of the curve y = (2+ 2x )3/2 between x=0 and x=2 is O 41/3 O 45/2 O 43/2 O 47/3 49/6 ООО…

A:

Q: Find unit tangent of curve r(t)=

A:

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

A:

Q: 11. Let h(z) = (arcsin(5z) + In(4 – z))27. Find h'(z). 12. Find in terms of x and y if arcsin(ry) =…

A:

Q: Find the length of the curve y = 4 1 between x 1 to x 2. %3D &x2

A: It is length of curve.

Q: Show that th equation of the tangent to the curve X 1승 +1-2(a 0,b + 0) at the point (a,.b) is 즈+-2 X…

A:

Q: y=Cx^2 and y=lnx find C where the graphs are tangent to each other

A: We have to find the value C.

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