Find the exact length of the curve. x3 4x' У 1 < x < 2 Find the exact length of the curve. х 3 8 4y2' 1

Q: Give the equations of the lines through the point (0, 9) that are tangent to the curve y x + 4 Use…

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

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Q: To find the length of the curve defined by y = 5x° + 8x from the point (-1,-13) to the point (2,56),…

A: Here the curve is given by y=5x3+8x x coordinate of the points (-1,-13) and (2,56) are -1 and 2…

Q: Find the equation for the tangent line of the graph of y=x^4 at (2,16)

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Q: The slope of the tangent line to the curve y at the point 6, is: 3 The equation of this tangent line…

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Q: Find equations of the tangent line and normal line to the curve  y= x sqrt x  at the point  (1,1) .…

A: Given curve: Let the slope of the tangent line to the given curve is m. And the slope of the normal…

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

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Q: 5. Find the equations of the tangent line and normal line to the parabola y = 2x² at the point…

A: Since, you have asked multiple questions , according to our guidelines we are supposed to answer…

Q: 25. Find equations of all lines having slope −1 that are tangent to the curve y 1/(x − 1). = 1/4…

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Q: 4 The slope of the tangent line to the curve y = X at the point 5, is: 5

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Q: Explain why Newton's method doesn't work for finding the root of the equation x3 - 3x +1 = 0 if the…

A: Given that

Q: Of the infinitely many lines that are tangent to the curve  y = −3 sin(x)  and pass through the…

A: Given :    Of the infinitely many lines, that are tangent to the curve y = −3 sin(x)  and pass…

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: Find the equation of the tangent line to the curve at the given point. (4,3) y= square root of 2x +…

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Q: Find the length of the curve defined by 2? = 2y3 from x = 0 to x = 4:|| %3|

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Q: Find equations of the tangent line and normal line to the curve at the given point. = x* + 9e*, (0,…

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Q: 1 Find the x-coordinates of all points on the curve y= 9x* – 48x° – 90x + 9x + 34 where the tangent…

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Q: x4 3x2 at x = 2 y = 4 2.

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

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Q: ind the curve that has slope (x+1)^2 and that passes through the point (−2 8)

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Q: 5. The slope of the tangent line at any point (x, y) on a curve is 10 – 4x, and the point (1, –1) is…

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

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Q: Find equations of the tangent line and normal line to the curve at the given point. y = x4 + 6ex,…

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Q: Find the slope of the tangent line to the curve 12(2 + )? = 625(x² – }) (a lemniscate) at the point…

A: Slope of tangent line is the first derivative of given curve at point ( x , y ) . Slope = dy / dx…

Q: Solve for z. 4 12

A: Solve for x

Q: Find y′ and the slope of the tangent line to the graph of the equation below at the indicated point.…

A: To find the slope of the tangent to the given function at the indicated point we need to find the…

Q: Find an equation of the tangent line to the curve 2(az² + y³)² = 25(x² – y}) - (a lemniscate) at the…

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Q: 9 Find the length of the segment 16 between the lines. y- 1-x + arcsinx of the curve -0, x

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Q: How many tangent lines to the curve y = x/(x + 1) pass through the point (1, 2)? At which points do…

A: The tangent lines to the curve y=xx+1 passes through the point (1, 2)

Q: The tangent line to the curve y = 1/3x^3−3x^2+9x+12 is parallel to the line 8x−2y=3 at two…

A: given: the tangent line to the curve y=13x3-3x2+9x+12 is parallel to the line 8x-2y=3 at two points…

Q: Find the equation of the tangent and normal to the curve

A: (1)y = x4-2x2+4Equation of tangent  - y = m1x+cwhere, m1=slope of the tangent = dydxDifferentiating…

Q: Find an equation of the normal line to the curve of y =    root x that is parallel to the line 4x…

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Q: Find the equation in terms of x and y of the tangent line to the curve r= 4sin 5θ and θ =π/3.

A: Given: r=4sin5θ  and θ=π3

Q: Find the length of the arc y = 8. 1 from X = 1 to x = 4. 4x www

A: Given

Q: -11 -, find the exact value of its x-coordinate. (Decimal approximation 61 A point in quadrant IIl…

A: A point in the 3rd Quadrant of the x-y plane has both x and y coordinates negative.  Equation of a…

Q: If the normal to the curve y=f(x) at the point(3,4) makes an angle of ¾Pi with the positive x-axis…

A: Answer of the provided qn in written has been provided below -

Q: Find the point(s) on the curve of y = 3x^4 − 4x^3 where the tangent line is parallel to the line…

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Q: 2. Find the equation of the tangent lines and the normal lines to the curve y = 2x² +3 at the point…

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Q: 11

A: A tangent is a line segment which touches the circle at only one point. A tangent is perpendicular…

Q: Find the tangent and normal line to the curve at the specified condition.  3x3 - x2 - 12x + 6 at…

A: Suppose we wish to find the equation of the tangent tof(x) = 3x3 − x2 - 12x +6 the points where the…

Q: Find equations of the tangent line and normal line to the given curve at the specified point. (1. )…

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Q: A tangent line to y=1/x^2 intersects the x-axis at the point A and the y-axis at point B. What is…

A: Please note: The line tangent to the given function intersects the x-axis at a point A and the…

Q: (b) Use the equation of the best fitting curve from part (a) to predict the distance required to…

A: (a)  The curve in  figure 1 perfectly fits the the data set

Q: Find the equation of a Tangent line to y = 2x2 – 5x – 1 that is parallel to line x + y –

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Q: 7. Find the slope of the tangent line at point (-2,2) on the curve flx) = 2x² + 3x. %3D

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Q: ind an equation of the tangent line to the curve at the point (3, 4).  y=(x-1/x-2)+2

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Q: Of the infinitely tmany lines that are tangent to the curve y=-4 sin(x) and pass through the origin,…

A: Answer is mentioned below

Q: Find the equation of the tangent line to the curve y=xlnx that is parallel to the line Y=1+3x.

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

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