curve y= sqrt(x+2) and the lines y=0 and x=7

Q: The curve y = ax2 + bx + c passes through the point (2, 32) and is tangent to the line  at the…

A: Given curve: y = ax2 + bx + c passes through (2,32) and  (0,0) line at the origin is tangent to the…

Q: ) Find the slope m of the tangent to the curve y = 9 + 5x² – 2x3 at the point where x = a. 10а + 6а?…

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Q: the slope of the curve 2y2=ax2+b at (1,-1) is -1.Find a,b

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Q: Sketch the curve f(x,y) = c together with Vf and the tangent line at the given point. Then write an…

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Q: Find equations of the tangent lines to the curve y = 6 n) at the points (1, 0) and (e, at the point…

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Q: Q3/ Line A with equation y = -8x – 18 is tangent to the curve with the equation y = 4x + 2x². Find…

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Q: Find the equation of the line tangent to the curve. y= -3x + x^2 +2 at the point (3,2) Include y= in…

A: The given equation of the curve: y=-3x+x2+2

Q: Q3: Find equations of all lines having slope (-1) that are tangent to the curve y = 1/(1-x)

A: y=11-x Also, the given Slope is -1

Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x, y) = |

A: To find - Point on the given line closest to the origin.

Q: Find the equation of the line tangent to the curve (x-2)^2=-4(y+3) at (2,-3)

A: Given data:     The expression for the equation of the curve is: (x-2)2=-4(y+3). The given point is:…

Q: Find the distance from the point Q to the line ℓ.

A: Given: Q=0, 1, 0, l with equation xyz=111+t-203.

Q: Find equations for the lines that are tangent and normal to the curve at the point (1,1).. x³ + y² =…

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Q: Consider the curve parameterized by a 3t2 15 and y= 2t3 15. Find equations for all tangent lines to…

A: We have to find the tangent to the parametric curve.

Q: Find equations of all tangent lines to the graph of y = 4x + 40x² + 125x + 118 which pass through…

A: We have given equation of graph y=4x3+40x2+125x+118. We have to find equations of all tangents which…

Q: Find the equation of the tangent line to the curve y=8ln(x3 −63) at the point (4,0)

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Q: Find the point on the line y=5x+3 that is closest to the origin (x,y)=(______)

A: Let (m,n) be the point on the line which is closest to the origin.Put n = m, y = n, in y = 5x + 3…

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 lines to the curve y = o mc) at the points (1, 0) and at the point (1,…

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Q: Find the equation of the tangent line to the ellipse 25x2+ y2 = 109 at the point (2, 3

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Q: The tangent line to the curve y = x3 - 6x2 - 34x - 9 has slope 2 at two points on the curve. Find…

A: Given,  The tangent line to the curve y=x3-6x2-34x-9 has Slope=2 at two points on the curve.…

Q: Find the coordinates of the point/s on the curve y = 2x2 which are closest to the point ( 9, 0 ).

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Q: 20. Does the line that is normal to the curve y = x² + 2x - 3 at the point (1, 0) intersect the…

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

A: Given : y=xx+1  pass through the point (1, 2) To find: The number of tangent lines to the curve  y =…

Q: ve passes through the point (0, 9) and has the property that the slope of the curve at every point P…

A: Topic:- application of integration

Q: a moving point is equidistant from the point (a,0,0) and the line x+a=0,y=0.Find the value of z^2

A: Let us assume that the point is = x,y,z The distance between the point a,0,0 and point x,y,z is:…

Q: 59. Find equations of both lines that are tangent to the curve 3x23x-3 and are parallel to the line…

A: First we find the slope of the tangent:Slope of the tangent is the derivative of the given…

Q: The equation of a curve is y = 4x³ + px², where p is a positive constant. Find the stationary points…

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Q: Sketch the curve f(x, y) = c together with Vƒ and the tangent line at the given point. Then write an…

A: Curve sketch for 2x2 -y = 13 Curve sketch for  3xy = -54

Q: Find the x-coordinate of the point where the curve y = x3 - x crosses the horizontal line y = 1.

A: Given:                                 y=x3-x and y=1  Let                                y=x3-x…

Q: 15. Determine the equations of two lines that pass through the point (-1,-3) and are tangent to the…

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

A: Differentiate the equation and get slope of tangent at (3,-4) ddxx2+y2=ddx252×3+2×-4×dydx=0dydx=34

Q: 2-x )Use the guidelines of this section to sketch the curve y3x-12VX.

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: Find the equations of the tangent lines to the graph of y=x²+6 that go through the point (0,-2) and…

A: Given problem:- Find the equations of the tangent lines to the graph of y = x2 +6 through the point…

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

A: Given, y=1x-1 Slope,m=-1

Q: Find equations of all lines having slope −3 that are tangent to the curve y=3/(x−4)

A: Equations of all lines having slope −3 that are tangent to the curve y=3x-4

Q: 2. Find the slope of the curve y 3x +1 at the point (-0). Draw the graph of the curve. KIVERSIT TLOU

A: Solution:Giveny2=3x+1  at -13,0To find Slope of the curve and Draw a graph of the…

Q: Plot the line y=1-3x and the curve y=34.6-x^2 (all under a square root). Find their point of…

A: Differentiation of a function at a point gives the rate of change of the function at that point. The…

Q: Find the distance between the point (1,1) and (3,9) along the curve y=x2

A: Given:The points (1,1) and (3,9) along the curve y=x2To find the distance we need use calculus as…

Q: 16. Find the equations of the tangent and normal lines to the curve 16x* + y* = 32 at its points of…

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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: Sketch the curve f(x,y) = c together with Vf and the tangent line at the given point. Then write an…

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Q: Use a graphing utility to sketch the intersecting graphs of the equations and show that they are…

A: Orthogonal curves are the curves whose tangent lines are perpendicular at every point of…

Q: Sketch the curve f(x,y) = c together with Vf and the tangent line at the given point. Then write an…

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Q: Find equations of both lines that are tangent to the curve y = x3 - 3x2 + 3x - 3 and are parallel to…

A: The given curve is represented by y = x3 - 3x2 + 3x - 3 and are parallel to the line 3x - y =…

Q: The y-axis and the line x = c are the banks of a river whose current has uniform speed a in the…

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Q: Find the equations of the tangent lines to the circle x2 + y2 = 1 which pass through the point (-4,…

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Q: Find a formula for the linear function whose graph is a plane passing through the point (4, 3, -2)…

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Q: Find equations of both lines that are tangent to the curve y=x3 -3x2+3x-3 and are parallel to the…

A: Given, curve y=x3 -3x2+3x-3 and tangent are parallel to the line 3x-y=15.

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.