What is the length of the curve y= x3/2+4 from the point (1,5) to (4,12)?

Q: a particle moves along a curve y = (2x² + 5x)°, calculatey (0) and what is the interpretation of the…

A: Let us considre the function y=f(x) The derivative the function is denoted as dydx=f'(x) Derivative…

Q: Find the points on the curve y = x4- 6x2 + 4 where the tangent line is horizontal.

A: y=x4-6x2+4 Differentiating with respect to x, we get dydx=4x3-62x+0=4x3-12x Now the tangent line is…

Q: Find length of curve: y=3x^(3/2) from x=0 to x=4

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Q: Find the equation of the tangent line to the curve y= (1+2x)2 at the point (2, 25). y = %3D

A: This question is based on application of Derivative.

Q: 4. Find the point on the curve y = 2x² – 12x + 5 where the tangent is horizontal.

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

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Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn

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

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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 points on the curve y = 2x3 + 3x² – 12x + 7 where the tangent line is horizontal.

A: Given,          The points on the curve y=2x3+3x2-12x+7 where the tangent           line is…

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 points on the curve y 2x3+ 3x2- 12x + 9 where the tangent line is horizontal. (x, y)…

A: The above question is answered below

Q: Find the equations of all tangent lines to the curve x² + 4y2 = 8 that pass through the %3D point…

A: The curve x2+4y2=8 that pass through the point (-4, 0). We have to find the equation of all tangent…

Q: Find the slope of the tangent line to the curve 4x + 4cy- 4y° 276 at the point (- 1,4).

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Q: The Normal to the curve 2x² – y² = 1 at the point (1,1)

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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: Determine the coefficients a, b, c, d that will make the curve y = ax3 + bx2 + cx +d passes through…

A: Given y=ax3+bx2+cx+d

Q: What is the slope of the line tangent to the curve x2 + y2 = 1 and parallel to the x=axis ?

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Q: Find the exact length of the curve on the given interval. Show at least 3 steps to justify your…

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Q: What is the slope of the tangent line to the curve 3x^3y^2−2y^3=−4 at the point (1,2)

A: To find the slope of the tangent line we need y' 3x3y2−2y3=−49x2y2+3x3(2y)y' - 6y2y'=0 [product…

Q: Make the curve y= ax2+bx+c pass through (2,1) and be tangent to the lane y= 2x +4 at (1,6)

A: The given curve passes through (2,1) ⇒1=4a+2b+c                                    (1) And the curve…

Q: Find the length of the arc of the curve 4y2 = 9x3 from the origin to the point (2,3v2).

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Q: The tangent of the curve x^2+y^2--7 * 2xy3DO at the point (1,1), is a. y-2-х. О b. y=x-2. O С.…

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Q: Find the line tangent to the curve x + yi = 4 at the point (3V3, –1). y = x- 4 Oy = x+4 y = O y= s…

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Q: Find the condition that the line ax+by =1 may be normal to the curve an-1y =xn

A: Given thatan-1y =xn Solution is as follows

Q: Find the length of the curve defined by y = 3z3/2 - 3 from x = 3 to a = 9. The length is

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Q: The slope of the tangent line to the curve y = 4/x at the point (3, 4/3) is: Must be written in y =…

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Q: Show that the curve of y = 2e2z + 3r + 2r3 has no tangent line with slope 2.

A: The given curve is y=2e2x+3x+2x3. Obtain first derivative as follows. dydx=ddx2e2x+3x+2x3=4e2x+3+6x2

Q: Find the equation of line tangent of y=x4-2x2+1 at (2,9)

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Q: Find the points on the curve y= x 4-6 x2 +4  where the tangent line is horizontal.

A: Find the points on the curve y=4x-6x2+4  where the tangent line is horizontal.

Q: Find the tangent and normal line to the curve at the specified condition. 12x2 - 20y2 = 55 parallel…

A: Given that the curve is 12x2-20y2=55 and the required tangent and normal line is parallel to the…

Q: 3) Calculate the length of the curve interval [-2₁2]. y = x²/2 on the

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Q: Find the are length of the curve 2x = 3 y over the interval from y=0 to y=1

A: To find: The arc length of the curve in the interval . Formula used: The arc length of the curve…

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 set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?

A: Given: y=2x+kat 2 distinct points

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 length of the curve 9y2=8x3 from x=o to x=12 when y>0

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

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Q: Find all points on the curve y = x³ + 2x² - 6x + 5 where the tangent is parallel to the line 2x + y…

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Q: The slope of the curve 2y = ax + b at (1,-1)is -1.Find a, b.

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Q: Find where the tangent line to y= (5x-1)2 (4x+7)3 is horizontel.

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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: Find the cuaatune of the curve dlefied by 1I cost Sin whore is

A: In the given question we have to find the curvature of the curve r→(t)=1rcost,1rsint,0where r&gt;0…

Q: The line that is normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) intersects the curve at what other…

A: Given thatx2 + 2xy – 3y2 = 0          …(1)On differentiating equation (1) with respect to x,

Q: Find the equation of a curve in the xy-plane that passes through (1,3) and -6x(2+y) V3 – 3x2 whose…

A: The formula for the substitution method for definite integrals is given by, where g'(x) and f(x)…

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: Find all points on the curve y =x3 +-x* + 6x² where the tangent is horizontal. 3

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Q: 12)What is the slope at (1,2) for curve define by xy^2=4?

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Q: 2. Find the curve that passes through the point (1, 3) and whose tangent line at (x, y) has slope

A: Solve for the curve

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.