Determine the area of the triangle formed by the tangent to the graph of the function y=3−x2 drawn at the point (1,2) and the coordinate axes (Figure 11).

Q: Write the equation of the tangent line to the graph exy + cos v = + COS at He %3D point (-0.3, 2.12)

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Q: Use implicit differentiation to find the equation of the tangent line at (1,3) to the ellipse…

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Q: use implicit differentiation to find an equation of the tangent line to the ellipse at the given…

A: Using implicit differentiation you can find the derivative without separating the dependent variable…

Q: Find the slope of the tangent line to the graph at the given point. (4 – x)y? = x³, (2, 2) Cissoid:…

A: Slope of tangent line =dydx(4-x)y2=x3differentiating w.r.t 'x'y2d(4-x)dx+(4-x)dy2dx =…

Q: Find an equation of the tangent line to the graph of the function at the given point.

A: y=tan-1x2 , 2,π4

Q: Find the tangent plane to the equation 5e*- öy at the point (12, 24, 5).

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Q: Find the equation of the tangent line at each point x=2cot(a), y=2sin2(a) (-2/(31/2), 3/2), (0,2),…

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Q: Find the equation for the tangent line of the graph of y = x° at (0,0).

A:

Q: Find the equation of the tangent line to the function h(x) = xv4 + 2x at x = 6. %3D %3D

A: Differentiate the function with respect to x to find the slope of the tangent line.…

Q: find an equation of the tangent line to the graph of the function at the point (6,1).   y=3^x-6

A: Equation of tangent is given by: (y-y1)=m(x-x1) where , m=slope of the curve. You can find solve by…

Q: Find the equation of the tangent line to the graph of the function f (x) = (x² + 8) (x – 3) at the…

A: The gradient of the tangent at any particular point is given by :     f(x) = (x2 + 8) (x - 3)…

Q: Find the length of the curve y2 = x3 from the origin to the point where the tangent makes an angle…

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Q: Find the equation of the tangent line to the curve y = IVI at the point (9, 27). %3D y = 9x(sqrt(27)

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Q: Find the equation of the tangent to the function y = cos(2x) at the point where x = л/4.

A: equation of a tangent line

Q: Find an equation of the tangent line to the astroid at the (3√3, 1).   x2/3 + y2/3 = 4

A: Given an astroid equation find the equation of tangent at a point.

Q: Determine the point on f(x)= 2x^e where the tangent is parallel to the line y= 2x-12

A: The equation of the curve is  f(x) = 2xe The line parallel to the tangent line on the graph of the…

Q: Find an equation of the tangent line to the curve at the given point. = sec X, (π/3, 2) y

A: The answer posted in the image would have been correct if the student had typed 23x instead of 23x…

Q: Find the equation of tangent to the circle x + y = 25 at the point (3, –4)

A: Equation of the tangent line

Q: Find the equation of the tangent line to the curve at the given point. y = 9x - 8Vx, (1, 1) %3D

A:

Q: Find an equation of the tangent plane to the graph of f(x, y) = xy3 + x2at (2, -2, f (2, -2)).

A: fx, y=xy3+x2 Partially differentiating with respect to x, keeping y as constant, we get fxx,…

Q: Find an equation of the tangent Iine to the ollowing curve at the point (0, 5). xe' + ye* = 5

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Q: Find an equation of the tangent line to the parabola y = x2at the point (2, 4).

A: To find the equation of the tangent line to the parabola y = x2at the point (2, 4). For the parabola…

Q: Find the coordinates of the points on the curve y= x' + 5x + 3 at which the tangent: makes an angle…

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Q: Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y-2y³ In the…

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Q: Find the slope of the tangent line to the graph at the given point. (4 - x)y? = x3, (2, 2) Cissoid:

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Q: Find the equation of the tangent line to the graph of x^2 * y^2 + 6xy =1512 at the point (-7,6)

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Q: Find the equation of the tangent line to the curve at the given point. y = /2x +1, (4, 3)

A: To find the slope, we find dy/dx at (4, 3) At (4, 3):

Q: Show that an equation of the tangent line to the graph of = 2 at the point (a, b) is given by a b.…

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Q: Find the equation of the tangent to the 2(x² + y²)² = 25(x² – %3D - y²) at (3,1)

A: Given : 2x2+y22 = 25x2-y2

Q: Find the slope of the tangent to a parabola y=x^3 at a point on the curve where x=2

A: Consider the following equation:

Q: Find an equation of the tangent line to the graph of the function at the indicated point. (2, 1)…

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Q: Find an equation of the tangent line to the curve at the point (0, 1). y = (1 + 3x)10 y =

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Q: Find the point (in the first quadrant) on the lemniscate 2(x2 + y²)² = 25(x² - y²) where the tangent…

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Q: Find an equation of the tangent line to the function y 3x2 at the point P(1, 3). = Soluti

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Q: Use implicit differentiation to find an equation of the tangent line to the ellipse at the given…

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Q: Find an equation of the tangent line to the curve x^(2/3)+y^(2/3)=13 at the point (−27,−8).

A: Given:

Q: Find the area of the circle whose center is at (2, -5) and tangent to the line 4x+3y-8=D0

A: Area of the circle = 9π sq.units

Q: Find the tangent line to the graph of x (x² +y² ) = y² at the point

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Q: (a) Find the equation of the tangent plane to the graph of : = (1,-1,5). + ) +4 at

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Q: Find the slope of the tangent to a parabola y=x^3 at a point on the curve where x=1/2

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Q: Use implicit differentiation to find an equation of the tangent line to the ellipse at the given…

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Q: Find the area A of the largest rectangle that can be inscribed under the curve of the equation below…

A: Given that the rectangle inscribed under the curves of the equation in the first and second…

Q: Find the equation of one of the tangent lines to the circle x2 + y2 = 52 that pass through the point…

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Q: Find the equation of the tangent line to the graph of y = arcsin a when V2

A: Note: as per our guidelines we are supposed to answer only one question.* *Kindly repost other…

Q: Determine the equation of the tangent line to the graph of y = y2 – x² at the points (분 ) and (블, )

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Q: Find the tangent plane to the equation 5e* бу at the point (12, 24, 5) Z =

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Q: Find an equation of the tangent plane to the surface at the given point. + 3x – z2 = 56, (5, -3, 2)

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Q: Find an equation of the tangent line at the given point. 2x1/2 + 4y −1/2 = xy, (1, 4)

A: Given,

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.