Trace the curve r =1/2(sinꝋcos3ꝋ)

Q: Area of a regim enilosed is by Curves y= 12 and

A: To find the area enclosed by the given two equations

Q: Find the equation of tangent and normal to the curve at (1, 1) 5x2 — 4x3у4 + 5у—Зх?у? %3D 2х + 3у —…

A: Given curve is 5x2-4x3y4+5y-3x2y2=2x+3y-5. To find the equation of tangent and normal to the curve…

Q: Draw a smooth curve starting at point C and tangent tő the line segments. Label the other end of the…

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Q: Find the normal to the curve y = 1 - x at the point (3, -8).

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Q: Find the equation of the tangent line and normal line to the curve y= √( x− 3) at (4,1).

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Q: Determine the slope of the tangent line to the curve A(x) = at x=-0.81 (answer in 2 decimal places,…

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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 length of curve - Vsec*t-1 dt -<ys=

A: To find- Find the length of curve x = ∫0ysec4t - 1 dt, -π4 ≤ y ≤ π4

Q: Estimate the slope of the tangent line at the point t= -2 for f(t) = 6t-3 (Give answer as a…

A: The given function is f(t)=6t-3 at t=-2

Q: Find the slope of the tangent line to the curve (a lemniscate) 2(2 + y²)° at the point (- 3, - 1) 2.…

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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: (A) Find the equation of tangent and normal to the curve 2x+y² (-2,-1). = 9 at

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Q: Plot the "astroid" y = (4 - x 2/3) 3/2 for 0 ≤ x ≤8. Show that the first-quadrant segment of each…

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Q: (a) Find the points on the curve where the tangent lines are horizontal or vertical.

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Q: What is the slope of the tangent line to the curve y = 3cos 2x at x= ? 4 Answer:

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Q: Find the lines that are tangent and normal to the curve y = tan x at the point (, 1)

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Q: ind the slope of the tangent to the curve 'x + y°x? = 6 at (2,1)

A: Here we need to find the derivative of the given function with respect to x

Q: Find the equation of the tangent line and normal line to the given curve at the specified point. y =…

A: The given equation is,

Q: Find an eqaution of the tangent line to the curve at the given point. y = √x, (1,1)

A: We have to find the equation of tangent line to the curve: y=x at the point 1, 1 We know equation of…

Q: Plot the curve x³ + y3 = 6xy together with the tangent to the curve at the point

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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: sketch the curve ƒ(x, y) = c together with ∇ƒ and the tangent line at the given point. Then write an…

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Q: 2. Find the equation of tangent and normal for the curve xsin2y = ycos2x at

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Q: Question 2

A: To determine the tangent line to the curve.

Q: Find the equation of the tangent and normal line at the point indicated. Sketch the curve. y = x –…

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Q: Find the equation of the tangent to the curve y=xcosx at x= 7. Use exact values in your answer f…

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Q: Determine the point on the curve y 16 a² where the tangent line is horizontal. A (2, 12) (-2, -12)…

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Q: II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT.

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Q: Find a point on the curve y=√x, where the tangent makes an angle of 45 degrees with the positive…

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Q: Find equation for the tangent line at (-l,1) , then an to the curve y= | sketch them togethor

A: Recall: Slope -point intercept form: y-y1=m(x-x1) ; where (x1,y1) is given point and 'm' is the…

Q: 1+lnx y =

A: y = 1+ln xx

Q: Find the point on the curve y = xe* where the %3D tangent is horizontal

A: Slope of tangent to the curve y=f(x) is defined as mT=dydx(x, y). Slope of horizontal tangent is…

Q: Find the slope of the tangent line to the curve r = 3-2sin(θ) at the point (3,pi).

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Q: Use the guideline of this section to sketch the curve 1. y = 1 + 1/x + 1/(x ^ 2)

A: To Sketch: y=1+1x+1x2 Explanation: (a). Domain and Range y=1+1x+1x2is defined everywhere except…

Q: Find the coordinates of the point in the first quadrant at which the tangent line to the curve 17x –…

A: The given curve equation 17x3-xy+y3=0               .....(1) Differentiate both sides with respect…

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: Sketch the curve y cu. = x sq.

A: Given the curve is y3 = x2 Put random value in the curve and we get the table which help to trace…

Q: Find the slope of tangent line to the curve r=3-cas(@) coste

A: Find dy/dx

Q: What is the slope of a line normal to the curve y=tan(x)/(1+tan(x)) at x=pi/4?

A: Given the equation of the curve y=tanx1+tanx To find the slope of the normal line to the given curve…

Q: Find the leguation tor the tangent to the at the point (1ら3). Curve y=x+3

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Q: 19. Find the lines that are (a) tangent and (b) normal to the curve y = x' at the point (1, 1).

A: Given curve: y=x3

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: = cost-sint, y = cost + sint;

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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 slope of the tangent line to the curve 42 4r 4y = 64 at the point (4, 2). Preview Get help:…

A: Obtain the derivative of the function with respect to x as follows.

Q: Find the tangent to the curve a"-'y = x"

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

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Q: image attached

A: Use chain rule:

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.