(2,4) The point A ( Pas lies on the Curve with equation Y=x At point A he curve nas gardient m. as show that m:lim. chany b) Deduce the value olm.

Q: 13. The range of the arcsin or sin(x) is: a) (0, 2.7) b)(0, 7 ) ) 0. d) 4 '4 e) 2'2 4

A: 13) Given

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A:

Q: e) sec mx – 1 lim

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Q: 8.) Let fx)= 2x³+3x +4 Use the limif definition of the derivative to calculate the derivative of f:…

A:

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A: Given: 2 Bezier curves are joined at the point p3. To explain what is the necessary for C1…

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A:

Q: f"(x) = 6x is the value of If the slope of the tangent of the function y=f(x) at the point A(1,7) is…

A: The slope of the tangent of the function y = f(x) at the point A(1, 7) is 5 and what f''(x) = 6x is…

Q: 96) = sech (sech 6x)

A: Formula Used:-(1) If g=f(h(x))then g'(x)=f'(h(x)) h'(x)(2) (sech (x))'=-sech (x) tanh (x)(3)…

Q: 6) a) show that Sx dx is divergent b) Show that Lim = 0. This shows we canuat xdx -- define = im…

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Q: 1. Let F = -yi + xj and let C be the unit circle oriented counterclockwise. (a) Show that F has…

A: When we integrate a vector-valued function over a path, the integral is referred to as the line…

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A:

Q: (XY) Cos E lim x.y) ->(I) 1-X -Cosy lim x2 y? Cx, y)->Co.d) 2x"+y4 How Can the function = x²+…

A: We will find out the required values.

Q: Sketch the graph of a function f that has all of the following properties: (i) (ii) (iii) (iv) f(1)…

A: Given (i) f(x)=f(-x) The curve should be symmetric with respect to y-axis. options (3), (4), (5) and…

Q: 6a) Let A be the parabolic arc defined by the equation y = 8x – x´ over the domain interval [0, 8].…

A: (a) Consider the given function. y=8x-x2 Now, draw the above function by using the calculator.

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A: Given Information:There is a set of curves on xy-plane. Objective:Find the graph of  among the given…

Q: 17. Let foxys = exy. Find the equation for the tangent plane to the graph of f at the point (1.1).

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Q: 28. Show that the graphs of y = tan x and y = cot x have nohorizontal tangents.

A: A horizontal tangent line is a mathematical feature on a graph located where a functions' s…

Q: Given the curve (x^2)y+ax+by=0 have three inflection points, where a and b are constants. a) Using…

A: We are given that the curve x2y+ax+by=0 has three inflection points, where a and b are constants.…

Q: For the curve r-y +2xy-y+1=0: a) Find the derivative dy/dx. b) Where do the horizontal tangent lines…

A: follow the next step

Q: o let fon= (x-1)? +2; xzl a find f-(x),domain range b) confirm fof cigraph t Uning yix using…

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Q: 3) Give an example of a function flz) which has the following properties. Justify your answer. b) A…

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Q: An example of cissoid of Diocles is r = sin 0 tan 0 whose graph is below. Show this curve has the…

A:

Q: 2=5x²- is EaJoxus Firnd an The curve 0ith equatio %3D kampyle of the Colled a equatien f at he peint…

A: Given : y2 = 5x4-x2

Q: 03) (Answer only two ): 4- Find the distance between the curve ( y=x+4) & line 0=x-4)

A: According to our guideline we can't solve multiple questions. so please repost the question…

Q: a) Evaluate: a tant t dt 4

A: ∫0π/4tan4tdt

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.