Identify and sketch the curve for: x^2+25y^2+100y+4=0

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

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Q: find a parametrization for the curve. the line segment with endpoints (-1, 3) and (3, -2)

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Q: Sketch the curve.

A: To Sketch the curve. Y = (x2-4)2x-4

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

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Q: Define tangency for general curves?

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Q: On the curve y3Dx2 ,find a point at which the tangent is parallel to the chord joining (0,0) and…

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Q: Describe the curves.

A: The curve in the first figure gives zero output for negative input it is excited at once and there…

Q: midpoint of

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

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Q: the guidelines of this section to sketch the curve: y = x+ – 8x

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Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. 4x² + 9y =…

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Q: What does it mean for two families of curves to be mutually orthogonal?

A: Two families of curve are said to be mutually orthogonal if they intersect at right angles. Angles…

Q: Use the guidelines of curve sketching to sketch the curve y = 1-x2 %3D

A: Given: y=x1-x2

Q: Find an eqaution of the tangent line to the curve at the given point. y = 4x - 3x2, (2,-4)

A: The given function is y=4x-3x2 and the point is 2,-4

Q: Find an equation of the tangent line to the curve y 9tanx at the point %3D

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Q: y=csinx  Identify the curves that intersect the curves under a right angle.

A: Given- y = c sinx To find- Identify the curves that intersect the curves under a right angle.

Q: Find the equations of the tangents to the curve x = 6t2 + 2, y = 4t3 + 2 that pass through the point…

A: Given data:     The first equation is: x=6t2+2. The second equation is: y=4t3+2. The given point is:…

Q: Find the tangent and normal lines to the curve ペー9ーチ at the Pomt (-62)

A: Given, The equation of the curve  x2-xy+y2 = 7  We have to find the equation of tangent and normal…

Q: ie point where x (-)- %3D

A: Maxima and minima: f(x)=x2+kxWe should find the value of f'(x) Then we calculate the value of x for…

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 an equation of the tangent line to the curve at thegiven point. y= 4x  - 3x2 ,    (2 ,-4)

A: we have to find an equation of the tangent line to the curve y=4x-3x2 at the point (2-4). as we know…

Q: Use the guidelines of this section to sketch the curve. х — 6 y = x2

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Q: Find the equation of the tangent line of funclion y= ²+1 23 -2 at (40,- 73)

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Q: Describe the condition for a curve to be rectifiable between two points.

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Q: Use the linear approximation to estimate

A: In this question, by using a linear approximation to evaluate the value of the expression using…

Q: Use the guidelines of this section to sketch the curve.   y = x √(5- x)

A: We can not have negative number inside square root So, 5-x≥0 x≤5  Let us make a table of values x…

Q: Determine the intervals of concavity and point of inflection of curve y=2x^4-3x^2+2x+1

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Q: Find the orthogonal trajectories to the family of curves:

A: Consider the given equation. x2=C-12y2lny2-1 Find the derivative of the function with respect to x.…

Q: What are the coordinates of the points in the graph of y2 – x² + 6x – 13= 0 in which the tangent…

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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: Use the guideline of this section to sketch the curve 1. y = 1 + 1/x + 1/(x ^ 2)

A: To Sketch: y=1+1x+1x2 Explanation: (a). Domain and Range y=1+1x+1x2is defined everywhere except…

Q: Find the areas fer theholLLawing egions: Regionenclosed by the Curve (r=2cosz0).

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Q: Find the points of intersection of the circle C of radius 3 centered at (-1, -2) and the line L with…

A: Want to find:                         the points of intersection of the circle C of radius 3…

Q: Find the tangent line to the curve 2y + " = ye"-2 at the point (2, ). %3D Please select file(s)…

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Q: Find the slope of the tangent lines on the curve y = 6x^3 +24x^2 -39x -43 at poins (-5, 2) and (1/3,…

A: We know that, The slope of the tangent line to the curve at a given point Px1,y1 is equal to the…

Q: Show that the curve y = 6x + 6x - 3 has no tangent line with slope 2.

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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 the curve length 1 X = 3 0² + 2) ?',0 < y < 4

A: In this problem, curve length of the given curve is to be determined

Q: Does this curve go through the point (-1, 1, -1)?

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Q: Find the slope of the tangent line to the curve y 3x-8x + 7 at the point (-1,2). -3 3. -4 4

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Q: Find the point on the curve y = 3x + 4 which is closest to the point (5, 0). Preview Preview

A: Let (x, y) be the point closest to the point (5, 0) We will calculate the distance between these two…

Q: Locate the points of inflection of the curve 4 ƒ (x) = x²e* -2+ V3 2+ V3 Option 1 Option 2 -2+ v2…

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Q: must

A: When a curve changes from concave down to concave up or concave up to concave down , that means…

Q: Describe how you would use the second derivative to determine a local minimum or maximum.

A: Given data is: How you would use the second derivative to determine a local minimum or maximum

Q: find the acute angles between the curves y=6x6-17x5-33x4-28x3 and y=95x2+79x+90 at their points of…

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Q: Find the differentual equatrion characterizing the family of curves described

A: Given that: ky=x2

Q: Find the tangent line at (-1,3) to the curve y* – 2x²y' – 27=0.

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Q: Find the exact length of the curve over the given interval. 2sxs3 4x'

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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.