Find the length of the curve y = 3/2 from a = 0 to a = 3.

Q: The diagram shows the curve y = ex and the tangent drawn at x = 2. AY X

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Q: Find an equation for the line in the xy-plane that is tangent and normal to the curve x³y² + y² = x…

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Q: Q4] (15Marks) Sketch the curve r cose. %3D

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Q: Find the equation of the curve y = f(x) as shown in the figure with line tangent to curve at P(x ,…

A: The slope of the tangent at a point on a curve is equal to the derivative of the curve at that…

Q: Find the tangent line to the curve C: r =t, y = t° – 3t at the point (3,0).

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Q: Find an equation for the tangent to the curve y = 18 at the point (1,6). 2. X +2 O A. y= - 4x + 10 O…

A: The equation of tangent  y = -4x +10  Hence option (A) is correct

Q: Find the length of the arc of the curve  where y=x^2+1 from the point  where y=1 to the point…

A: Formula to find the required arc length. Formula to find the arc length for the limits of y is…

Q: ind the tangent and normal to the curve y =2e at the point where the curve meets the y – axis

A: Find the equation of the tangent

Q: 5) Sketch the curve X = e', Y = e?t + 1

A: Given, The curve  X = et  and  Y = e2t+1 We have to sketch the curve.

Q: Find the length of the curve y2 = ln x, -1 ≤ y ≤ 1.

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Q: Consider the curve defined by the equation y3+xy+2=0.  Show that there are no points on this curve…

A: Consider the given curve define by the equation:

Q: Consider the curve defined by the equation y³ + xy + 2 = 0. Show that there are no points on this…

A: Given Equation of curve   y3+xy+2=0  ---(1)

Q: Find the tangent line to the curve C: r =t, y = t – 3t at the point (3,0)

A: dydx=dydtdxdt=3t2-32tx=3 at t=±3 so there are two slopes tangent…

Q: Find the exact length of the curve y = ln(sec(x)),   0 ≤ x ≤ ?/6

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Q: Find the tangent and normal to the curve y=2e-x/3 at the point where the curve meets the y-axis

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Q: Find an equation of the tangent line at a point (0, 0) on the curve x =t- 100, y = t2– 10t.

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Q: Find an equation for the line tangent to the curve x= 2sin(t), y= 4cos(t) at the point defined by…

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Q: Show that the exact length of the curve below is y = Vr - r² – sin ¬1 (V7)

A: SOLUTION-

Q: Find the equation of the tangent and normal to the curve y = x + x at(0,0).

A: We have to find the equation of tangent and normal for the curve: y=x+x23 at the point 0, 0 We know…

Q: dy Find for the curve 49 + 6x° = 3 + sin(7x-y). da

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Q: Find the length of the curve y = ln(sec x ), x is an element of [0, pi/4]

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Q: The line y = mx + 1 is a tangent to the curve y2 = 4x .Find the value of m

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Q: Find the exact length of the curve. y = ln (1 − x2),  0 ≤ x ≤ 1/3

A: We need to use the chain rule to find dy/dx.

Q: 10. Find the exact length of the curve y = In(sec x),0 < x<T/4 %3D

A: This is a problem related to integration of the function. Based on the integral formula we will find…

Q: Q3/Find the tangent to the curve x+ xy+ y' = 1 at (1,-1).

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Q: Find an equation of the tangent line to the curve at thegiven point  y =  e x  / x…

A: Given curve is y=exx To find: Equation of the tangent line to the curve at point (1,e). Solution:…

Q: Find the length of the are of the curve п x=e' sint , y=e' cost from t-0 to t=:

A: Given: x=etsint, y=et cost from t=0 to t=π2

Q: Find the equation of the tangent line to the curve x=t2−2t, y=t2+2t at the point t=2.

A: Given equation of curve is Now,

Q: Find an equation for the tangent curve x= 3e^t, y= 5e^-t at t = 0.

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Q: Determine the tangent to the curve 3y2 = x3 at (3,3) and calculate the area of the triangle bounded…

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Q: 4. Consider the curve given by r³ + y³ = 9ry. Find the equation of the tangent line at (4,2).

A: To find the slope of the tangent we need dydx at (4,2)…

Q: Find the exact length of the curve. y = ln(cos x),   0≤ x ≤ π/3

A: Formula used: L=∫ab1+dydx2dx

Q: Find the equation of a curve having a slop by dy xy? у 3 ху? —, x > 0 dx and passing through the…

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Q: Find the length of the arc of the curve y = ln x over the interval: 1, 7| . Round the answer to four…

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Q: Find the tangent and normal to the curve a2y=3x at (a,a)

A: Equation of tangent to the curve at x0,y0.                y-y0=m(x-x0) Equation of normal to the…

Q: Plz solve this now in 10 min and take a thumb up plz

A: We have to solve the problem

Q: Find the length of the curve y = ln (sec x), 0 <I<÷.

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Q: Find an equation of the curve y = f(x) if y^n = 6x and the tangent line to the curve at (1, 2) is…

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Q: Evaluate the length of the curve: y = 3x + sinx, 0 ≤ x ≤ 1.

A: Let L be the length of curve  F(x) = 3x + sinx

Q: For the implicit curve y + xy + x2 = 3, find a point on the curve where the tangent line is…

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Q: Find the point(s) on the curve t3 3t, y 2t2 +t 2 x = - where the slope of the tangent line is equal…

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Q: Find the point on the curve y=/2 for which the tangent ine to the curve is perpendicular to the line…

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Q: Find the point where the tangent line to the curve c(t) = (8t2 – 6, 3t2 – 12t) is horizontal. (х, у)…

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Q: メ*+\ for what Value sss of x ,t he curve y= 3 X has horizontal tangent

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Q: Find the slope of the tangent to the curve y² In(x) + x²y = 4 at (1, 4). %3D Need Help? Read It

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Q: Find the length of the curve r(t) = for 0 ≤ t ≤ 2π Enter the exact value.

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Q: Find the equation of the tangent line of the curve y = sin x + cos x at the point A(, v2). 4'

A: Point-Slope form of equation of line : y-y1 = mx-x1 where m is the slope of the line and x1, y1 is…

Q: At what points on the given curve x = 4t?, y = 5 + 8t – 21² does the tangent line have (x, y) =…

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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.