Find length of curve: x= (y^(3/2) / 3 ) - y^(1/2) from y=5 to y=11

Q: Find the shaded area of diagram that shecked by curve y = x2 + 2x and the line y = -x.

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Q: Differentiate (x-2)2+(y-3)2=9 at (7/2, ((6+3√3)/2)). Then use it to determine the equation of the…

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Q: Find the equation of the tangent line to the curve x 1- cose, y = 0 -sin0 at 0=. 4

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Q: Find the tangent line approximation for √1 + x near x = 5. y = |

A: Given 1+x

Q: Find the points on the curve y = 2x + 3x2 - 12x + 7 where the tangent line is horizontal. (х, у) %3D…

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Q: Find the points on the curve y = x3 + 3x2 - 9x + 8 where the tangent is horizontal. smaller x-value…

A: Explanation of the answer is as follows

Q: Find the tangent line approximation for √1+ x near x = 5. y = ||

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Q: Find the points on the curve y = 2x3 + 3x2 12x + 2 where the tangent line is horizontal. (х, у) %3D…

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Q: Find the slope of the tangent line to the curve - 32 + 2ry-y = 0 at the point ( 1, – 1).

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

A: Given curve is 9y2=4x3, and the point is 3,23.   The objective is to determine the length of arc of…

Q: as y y = f(x) (10, 4) Tangent line (4, 2) ive your answer to three decimal places.)

A: G

Q: What is the slope of the tangent line to the curve y=3cos2x  at x=π/4 ?

A: First find out derivative then put the value

Q: Find the tangent line at (-1,3) to the curve y* – 2xy – 27 =0. ,3 |

A: Given- y4-2x2y3-27=0 To find- The equation of the tangent at the point -1,3 to the above curve.…

Q: The second derivative of curve: y = acosx, will be Select one: acosz acosx O -asinz O asinx

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Q: Find the equation of the tangent line to the curve y = IVa at the point (16, 64). %3D y =

A: The standard form of the tangent line helps to find the required equation of the line. The standard…

Q: The slope of the tangent line to the curve y=2eUXcos(-6x) at x-0 is

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Q: x = esine y = ecose

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Q: Find the points on the curve y = 2x3 + 3x2 – 12x + 6 where the tangent line is horizontal. (х, у)…

A: We will find the points on the curve where the tangent is horizontal.

Q: Find the points on the curve y = 2x' + 3x² – 12x + 1 where the tangent is horizontal. -

A: As per the instruction, we will be answering the first question. For (51), Given: y=2x3+3x2-12x+1.…

Q: What is the slope of the tangent line to the graph of y = cot-1 V2x +Iat the polnt where z = 0?

A: Slope of the tangent is the derivative of y at x=0

Q: Find the exact length of the curve. 1 y = 1 + cosh(8x), 0 ≤ x ≤ 1 8

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Q: For the curve 3e arcsin (y) + 2 (x² + y²) = 2, find the slope of the tangent line at the point…

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Q: Find the points on the curve y = 2x + 3x2 – 12x + 7 where the tangent line is horizontal. (х, у) %3D…

A: Hhxd

Q: Find the equation (in terms of x and y) of the tangent line to the curve r=4sin2θ at θ=π/3. y=?

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Q: Find the slope of the tangent and normal to the curve  y=2x2+3sinx at x=0

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Q: 2. Find the equation of tangent and normal for the curve xsin2y = ycos2x at

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Q: Inc is perpendicular to the linez =7 at the point where The tangent line to the graph of y

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the points on the curve y = x + 3x2 9x + 1 where the tangent is horizontal. %3D smaller x-value…

A: The given function is y=x3+3x2-9x+1

Q: Find the points on the curve y = 2x3 + 3x2 – 12x + 3 where the tangent line is horizontal. (x, v) =…

A: Solve the following

Q: Find the points on the curve y = 2x3 + 3x2 – 12x + 1 where the tangent line is horizontal. (х, у)…

A: Solution ) given f(x) = y = 2x3 + 3x2 - 12x + 1 f'(x) = 2 × 3 × x3 - 1 + 3 × 2 × x2 - 1 - 12 + 0…

Q: Find the slope of the tangent line to the curve `-3 x^2 + 3 xy + 4 y^3 = 8` at the point (4,2)`.…

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Q: Determine the equations of the tangent and normal to the curve y=2xex at (0,0)

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Q: Find the points on the curve y = 2x3 + 3x2 – 12x + 6 where the tangent line is horizontal. (х, у) %3…

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Q: Find the slope of the tangent line to the curve x + xy – y = 23 at the point ( – 3, – 2). -

A: The given function is x2+xy-y3=23 The point is x0,y0=-3,-2

Q: Find the tangent line at (-1,3) to the curve y* – 2x*y' - 27=0.

A: Given, The equation of the curve    y4 -2x2y3 -27 = 0  We have to find the  tangent line at -1, 3 .…

Q: Find the tangent line to the curve y = 2x - x2 at (2,0)

A: The equation of the curve is given by y = 2x-x2 The point is x0, y0 = 2, 0 Formula Used: The formula…

Q: Find the slope of the tangent line to the curve y = arctan(13x +e) at the point (0, 7/2).

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Q: Find an equation of the tangent line passing through the curve defined by y%3esinxcosx at x=,

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Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 6  where the tangent line is horizontal.

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Q: Determine the point(s) where the tangent to the curve is horizontal: y = (x2 + 2x + 1)(x2 + 2x + 1)

A: Given problem:- Determine the point(s) where the tangent to the curve is horizontal:   y = (x2 + 2x…

Q: How can we find the slope of the tangent line to the parabola y = x2 at the point?

A: Consider the following equation of parabola: y=x2 Differentiate y with respect to x: dydx=ddxx2=2x

Q: Find the equation of tangent and normal for the curve xsin2y = ycos2x at ,

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Q: The slope of the tangent line to a curve at any point is (5x² - y) ex+y If the curve passes thru…

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Q: At what point of the curve y = cosh x does the tangent have slope 1?

A: Given curve is: y=coshx

Q: Find the points on the curve y = 2x3 + 3x2 – 12x + 3 where the tangent line is horizontal. (х, у)…

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Q: What are the cordinates of the point on the curve /(x)= -2x where the tangent is horizontal?

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Q: Find the points on the curve y = 2x3 + 3x² – 12x + 5 where the tangent line is horizontal. (х, у) )…

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Q: Approximate the length of the curve accurate to two decimal places

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Q: Find the tangent line to the curve ry = a +y+1 at (3,2)

A: Given data: The expression for the given curve is xy=x+y+1. The given point is (a,b)=(3,2).…