Trace the curve: r^2 = 4cos^4ꝋ tan^2ꝋ

Q: Differentiate. y = (arcSin 2x)2

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Q: Find the shaded area of diagram that shecked by curve y = x2 + 2x and the line y = -x.

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Q: Sketch the curve.

A: To Sketch the curve. Y = (x2-4)2x-4

Q: Find The derivative of The functiin' toy do not nud to Simpliy The answer' y= arcscc (In 69) +…

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Q: Use implicit differentiation to find the equation of normal line to the circle y2 + x2 = 1 at the…

A: The solution for the above question is as shown below.

Q: Find the points on the curve y = 2x + 3x2 - 12x + 7 where the tangent line is horizontal. (х, у) %3D…

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Q: Which image shows a tangent line?

A: Tangent is a line that touches the circle only at a single point.

Q: Find the second derivative of the funcion. y%3D

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Q: ズ Find an equation of the tangent line to the curve y= 8 arccos at the point (1, 7). 2

A: we have to find the equation of the tangent to the curve y at (1, π)

Q: Explain the main property of tangent function?

A: The tangent function is an odd function, and its graph is symmetric with respect to the origin over…

Q: Define tangency for general curves?

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Q: Explain how limits arise when finding the instantaneous rate of change of afunction or the tangent…

A: The average rate of change of f(x) with respect to x as x changes from…

Q: Estimate the slope (in y-units per x-unit) of the tangent line to the curve.

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Q: Determine the point on the curve where the tangent is horizontal.

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Q: Describe the curves.

A: The curve in the first figure gives zero output for negative input it is excited at once and there…

Q: Find the slope of the tangent line to the ellipse 1 at the point 25 slope =

A: Here the equation of ellipse is x29+y225=1 and the point is (m,n)We have to find the equation of…

Q: midpoint of

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Q: Find the derivative dydx of Galileo’s spiral.

A: To find: Derivative of Galileo's spiral

Q: Estimate the slope (slope = rise/run) of the tangent line to the curve.

A: answer is in next step . please give a like !!

Q: The second derivative of curve: y = acosx, will be Select one: acosz acosx O -asinz O asinx

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Q: Determine point(s) where tangent lines to the curve is vertical / horizontal.

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Q: x = esine y = ecose

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Q: calculate the derivative

A: Given  The chain rule of derivative is given by The derivative of the hyperbolic function sech(x)…

Q: Find the tangent and normal lines to the curve ペー9ーチ at the Pomt (-62)

A: Given, The equation of the curve  x2-xy+y2 = 7  We have to find the equation of tangent and normal…

Q: Find the tangent line of the curve (- 31,1-2)at the point (2,14)and estimate y0 so that (2.1,y0)is…

A: given curve is                                                                     x=t3-3ty=t4-2…

Q: ie point where x (-)- %3D

A: Maxima and minima: f(x)=x2+kxWe should find the value of f'(x) Then we calculate the value of x for…

Q: Write the equation of the tangent line to the curve = 2 at the point (1,1). .3

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Q: to find slop

A: Given : f(x)=x2-6x To find: Slope at the given point

Q: Average velocity is equal to the slope of a secant line through two points on a graph. Which graph?

A: Average velocity formula is:

Q: For the curve 3e arcsin (y) + 2 (x² + y²) = 2, find the slope of the tangent line at the point…

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Q: Determine the equation of the slope of the line tangent to y = tan(x) using the 4-step rule.

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Q: Describe the condition for a curve to be rectifiable between two points.

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Q: Find the linear velocity of a point on the edge of a wheel rotating 35 times per minute. The…

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Q: Find the slope of the Curve r=-I+Sine atthe points 8=0,T-

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Q: Find the points on the curve y = 2x3 + 3x2 – 12x + 1 where the tangent line is horizontal. (х, у)…

A: Solution ) given f(x) = y = 2x3 + 3x2 - 12x + 1 f'(x) = 2 × 3 × x3 - 1 + 3 × 2 × x2 - 1 - 12 + 0…

Q: Now, find the equation of the tangent line to the curve at (1, 1). Write your answer in mx +b format

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Q: Find the area of the largest rectangle that can be inscribed in a circle of radius 10 inches. use…

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Q: Find the tangent line to the curve 2y + " = ye"-2 at the point (2, ). %3D Please select file(s)…

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Q: At what point is the tangent line to the curve y = 2x to the line x - perpendicular – y – 8 = 0?…

A: Let the point is (a, b), so the slope of the tangent line to the given curve can be determined as,…

Q: Find the point in the first quadrant where the line y=2x intersects a circle of radius 3 centered at…

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Q: What are the cordinates of the point on the curve /(x)= -2x where the tangent is horizontal?

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Q: . What is the slope of the line tangent line to the curve x?y = y? – 6x when x=2?

A: This question is taken from the tangent and normal in which we have to find the slope of the tangent…

Q: ength of the curve 1 1 < x < 2. 6 10x3 +

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Q: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x-coordinate…

A: It is given that the x coordinate increases at a steady 10 m/sec. dxdt=10msec. The equation of…

Q: What is the derivative OF a Arcsin X y= 3

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Q: Sketch the curve and find the axis. y = Sinx; [0,] 2

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Determine equation of tangent line to the curve at given point.

A: Given curve is f(x)=7x+2f(1)=7(1)+2=3 Differentiate f(x) with respect to x.…

Q: What is the slope of the line tangent to the curve  y=7cosx when x=π/4?

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Q: What is the equation of the normal to the curve which is a circle with center at origin and radius…

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Q: Approximate the length of the curve accurate to two decimal places

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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.