3x + xy? 2y + x?y dy dx

Q: 4. Find the equations of the line tangent to the intersection of the surfaces z = x´ + 2y and

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Q: 1 find the length of the curve x = 7y* + y2, from y = 1 to 24 y = 2.

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Q: Find the exact length of the curve.10. 36y 2 = (x2 – 4)3, 2 ≤ x ≤ 3, y ≥ 0

A: Given :                36 y2  =  ( x2 - 4)3  To find :                  The exact length of the…

Q: 2. Eliminate the parameter and find the equation of the curve in x,y Curve: x=1-sin?t, y= cost, 0 <t…

A: topic - equation of curve in x,y

Q: 2.) Find the acute angle between the given curves y² = 2x and 4x²+ 4y² +5y=0

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Q: Find the coordinates of the point(s) on the curve y = Va + 3 that are closest to the point (8, 0). O…

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Q: Find the exact length of the curve. y = In(sec(x)), Osxs n/4

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Q: Find the exact length of the curve. y =  3 +1/2 Cosh 2x,   0≤ x ≤ 1

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Q: Find the exact length of the curve. = 글Vy (y-3), 16 sys 25 X =

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Q: 1 Find the length of the curve x= from y 1 to y=2. +. 16y

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Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = 4t2, y = t3 - 1

A: We have given curves; y = ƒ(x) . x = 4t2, y = t3 - 1

Q: 2. Find the lengths of the given curves: a) y = x/2 -x2,1sK< 4 L = V1+f(x)*dx 3

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Q: tind the point on the curve y=Jx that is closest to the point (3,0).

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Q: Find a point on the curve y = x² that is closest to the point (18, 0). %3D AY y =2 (x, y) (18, 0)

A: Find a point on the curve y=x2 that is closest to the point  Here use distance formula…

Q: 10. If the curves f(x, y) = 0, y, z) = 0 touch, show that at the point of contact, dr dø dr dø dy dx…

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

Q: 1. Find the length of the curve: y = x/2 , x = 0 to x = 4

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Q: y = 1/2 (e² + e^¹), − 1 ≤ x ≤1

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Q: The Normal to the curve 2x2 – y? = 1 at the point (1,1) is: %3D 3 y =-*+ y =x+ y = 2x + 1 %3D P. y =…

A: To find The equation of normal to the curve 2x^2-y^2=1 at the point (1,1)

Q: ind the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -1,…

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Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: The curves y = In x and y = 3x² have parallel tangent lines at x = A) ± √/ B) C) √6 E) 2

A: Two lines have parallel tangent if slop at the point is same.

Q: Find the point on the curve y = Vx closest to the point (1,0).

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Q: y = e*, 0<z<1.

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Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: At how many points do the curves r₁ (t) = ((t+1)², -t2- 2t, t+2) and r₂ (t) = (1 − t², t, t)…

A: This is the problem of parametric equations and the theory of curves.

Q: Find the length of the curve y = V- from z =1 to r = e. 3

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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 curve r= e2θ, 0≤θ≤2

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Q: 4 Find a. the equations of the tangents to the circle x +y + 4x – 2y – 24 = 0 at the points where…

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Q: 3 Find the length of the curve y = x² – 2 from x = 0 to x = 4.

A: Given curve is y=x32-2 Upon differentiating we get dydx=32x12 We know that length of…

Q: Find the exact length of the curve. y = In(sec(x)), 0 <x< a/6

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Q: The length of the curve y = Ey3/2 between x = 0 and X 1 is %3D

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Q: The length of the curve defined by x =(v² + 2)E, y € [0,1]. Select one: none O 12

A: Arc length of the curve x=g(y), y∈[a, b] is, S=∫ab1+(g'(y))2 dy

Q: Find the length of the curve y = 4 1 between x 1 to x 2. %3D &x2

A: It is length of curve.

Q: Find the equations of the tangent and normal line 4x2 + y? + 8x + 2y = 20 at x = -3 %3D

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Q: Find the exact length of the curve. x = (2y + 1)3/2, 0<y<3

A: Differentiating with respect to y, we get

Q: Find the length of the curve y = a +; from a = 0 to x = 1. O None 5/2 O6/2 3 O4/2 3. 3

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Q: Consider the curve given by y2+xy=x3-(2y/3)+(3x2/4) a) Find all the points (x,y) on this curve…

A: Given is the equation  y2+xy=x3-2y3+3x24..............................(1) The objective is to find…

Q: SOLVE STEP BY STEP Evaluate the length of the curve x = 5 - Vy+1 , 0<ys 3

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Q: b) Find the points on the curve 2 17x + 12xy + 8y“ = 100| that are farthest away from the origin…

A: Substitute x = rcosθ and y= rsinθ

Q: Find the exact length of the curve. x = Vy (y - 3), 9 < ys 25

A: It is given that x=13yy-3, we need to find the exact length of curve.

Q: Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

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Q: Find the exact length of the curve. y = In(sec x), 0s x s a/3

A: This question is based on application of Derivative.

Q: The curve y = ax? + bx +c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: Explanation of the answer is as follows

Q: The length of the curve defined by x =÷(y² + 2)E, y E [0,3] %3D

A: Arc length=∫ab1+dxdy2dy

Q: Find the lengths of the curves x = (y/4)2 - 2 ln (y/4), 4 ≤ y ≤12

A: Given equation of the curve - x = y42-2lny4           .....................(1)Given intervals = 4,…

Q: Find the exact length of the curve. Y=y4/8 + 1/4y2, 1 less than or equal to Y less than or equal 2.

A: Given: Y=y48+14y2 , 1≤y≤2 As, the length of the curve, L is given by: L=∫ab1+dydx2dx According to…

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.