Find the exact length of the curve. y = 4 글2-글 In(x), 1 < x < 4

Q: Find the length of the curve y ' = 8x from x=1 to x = 8 www

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Q: Find the slope of the curve, equations of the tangent and normal lines to the given point. 8x y at…

A: Solution

Q: Find the point(s) on the graph y = x3 where the line through the point (4, 0) is tangent to y.

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Q: At what point is the tangent line to the curve y° = 6x² perpendicular to the line x y - 9 = 0? NOTE:…

A: To find the point on the curve y3=6x2 where the tangent line is perpendicular to the line x-y-9=0 .…

Q: Find the exact length of the curve = √(y - 3), 1 ≤ y ≤

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Q: Find the slope of the tangent line for the curve r=3+5cosθ when θ=π/6

A: Concept - If a function f(x) is given then slope of the line tangent to it at x=a is given by -slope…

Q: For what values of a and b is the line – 2x + y = b tangent to the curve y = ax? when x = 3? - - a =…

A: Given: To determine the values of a and b is the line -2x+y = b tangent to the curve y=ax2 when x =…

Q: find equation for the lines that are tangent andnormal to the curve at the given point. ex + y2 = 2,…

A: Given: Equation of curve ex+y2=2 and the point 0,1, To find: Equation of tangent and normal line to…

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: Given curve is The point (-1,3) lies on the curve if it satisfies the equation of curve Therefore,…

Q: Find for x? + x +y² + 2 = 3xy the lines that are tangent and normal to the curve at point (3,2).

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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…

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Q: Find the slope of the tangent line that passes through point (1, 2) to the graph 8y³ + x²y O-2/97…

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Q: Find the slope of the tangent line to the curve — 4г* + 4гу + 4у — 92 at the point ( – 1, 3).

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Q: 17. Given the curve y = 3x³ – 4x² +7, find the slope of the tangent line at the point when x= 3.

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Q: Find the exact length of the curve y3 = 22 from (-1,1) to (8, 4).

A: Use formula of length of curve

Q: find equations for the lines that are tangent,and the lines that are normal, to the curve at the…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the slope of the tangent line to the graph at the given point. (4 - x)y? = x3, (2, 2) Cissoid:

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Q: 1. y = 2x2-5 at ( 2, 3) %3D

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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 length of the following curve. y = 3x 2) fromx = 0 to x= 8

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Q: Find the length of the are of the e curve from point K(8,8) to M(!,5, -Y= -4

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Q: Find the slope of the tangent line to the graph at the given point. (x2 + 4)y = 8, (-2, 1)

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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 Data The equation is:  The point is: (-2,1)   Substitute the point (-2, 1) in the given…

Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangents…

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

Q: For what point on the curve of y = 3x - 6x is the slope of a tangent line equal to 0? %3D

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Q: The family of curves orthogonal to ye2x = c is the family of curves whose general equation is?

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Q: Find the slope of the tangent to the curve y = 25* at the point (1, 32).

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Q: Find the exact length of the curve. + 4х 1 < x < 3 y

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Q: A curve like Y = is called a serpentine. 1+2x2 3 n equation of the tangent line to this curve at the…

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Q: 2. Find the equation of the line that is tangent to the circle x + y = 25 at the point P(3,4)

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Q: Sketch a curve with the following properties. 0, for x> 12

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Q: Find the equation of the tangent and normal line using the stipulated conditions   1.) y = x2 - 5x…

A: Given the equation is y = x2 - 5x The point of intersection line y=6 The equation of the tangent is…

Q: 2. Find the length of the curve y=- 1 from 1<x<2. 8 4x?

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Q: a) Calculate the length of the curve defined by x = -3 )on the interval 1 sys9.

A: (a) Given that, x = 13 y (y-3) on the interval 1 ≤ y ≤ 9   We have to calculate the length of the…

Q: Find the length of the curve defined by y = 4x3/2 + 11 from x = 2 to x = 8.

A: We will differentiate the function and use the arc length formula.

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

A: Given curve, y=14x2-12lnx   ;  1≤x≤4

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: Now when x = 3, we get Therefore the point (3, -4) is on the given curve. a). Slope of the tangent…

Q: 5. Find the point on the parabola y=-x+3x+4 where the slope of the tangent line is 5.

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Q: What is the slope of the tangent line that touches the graph of In(y) + eA-=3y-4x at the point 3. 5

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Q: Find the length of the curve : y = + from x = 1 to x = 3 - 3 4x

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Q: Verify that the given point is on the curve and find the lines that are (a) tangent and (b) normal…

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Q: Find an equation of the tangent to the circle x 2 + y 2= 25 at the point  (3,4)

A: x2+y2=25 Differentiating with respect to x, we get 2x+2y·dydx=0⇒2y·dydx=-2x⇒dydx=-xy Now slope of…

Q: or the curve x²y²=9 at (1,3) find the equation of normal line

A: Given: x²y²=9

Q: Find the slope of the curve, equations of the tangent and normal lines to the given point. y = x3 –…

A: We have to solve the problem

Q: Find the length of the curve over the given interval.

A: Answer and explanation is given below

Q: 1 Find the length of the curve ソ= 9 from x =1 to x=2. 28x7,

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Q: Find the slope of the tangent line to the graph at the given point. (x² + 4)y = 8, (-2, 1) Witch of…

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