Show that the inflection points of the curve y=sinxxy=sin⁡x/x lie on the curve y2(x4+4)=4.

Q: Find the equation of the tangent line to the curve J (x) = ta n(x) in point-slop %3D at x =

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Q: Find the equation of the tangent line at the given value of x on the curve. 2y (x- 3) + xvy = 3; x=3…

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Q: Find an equation of the tangent to the curve x = 5 + In t, y = t2 + 2 at the point (5, 3) by two…

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Q: Find the equation of tangent and normal to the curve x sin 2y = y cos 2x at 4 2

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Q: Find the equation of the tangent line to the curve y=2sin(x) at the point (pi/6, 1) in y=mx+b

A: Using equation of tangent formula.

Q: Find the equation of the tangent line at the given value of x on the curve. 3y +xy-y%3D375X"; x-1…

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Q: Find the slope of the tangent line to x2y2+x sin(15y) = 4 at any point (x, y) on the curve.

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Q: tangents are drawn from the origin to the curve y=sin x.Prove that their points of contact lie on…

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Q: Find the equation of the tangent line to the curve y = sin x cos x at x = π/4 (Coefficients must be…

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

A: Please refer the attached image for complete solution.

Q: The Normal to the curve 2x² – y² = 1 at the point (1,1)

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Q: 3. Find the slope of the tangent line to curve x=2sin2t, y = cos4t when t=-

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Q: Find the equation of tangent to the curve given by x=d' cos' y-a sin'o at point VE(x+ y) = a b)…

A: x=a3cos2∅y=a3sin3∅

Q: Find an equation of the tangent line to the curve at thegiven point.   y = ex   / x  , (1, e)

A: Given: y=exx,1,e. for finding tangent at given point we need slope of tangent at that point  so,…

Q: Tangents are drawn from the origin to the curbe y=sin x.Prove that their points of contact lie on…

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Q: Find the equation of the tangent plane to z = In(x²y) – x/ỹ at (-,4).

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Q: Find the equation of the tangent line to the curve y = ex/x + ex at (0, 1).

A: Given that curve  y = exx+ex at (0, 1). The slope of tangent any point on the curve is given by its…

Q: Find the tangent line at (1, 0) of the curve xe^y = 2 sin(xy) + cos y.

A: Slope of the tangent is given by the derivative of the function at that point. So first we will find…

Q: Find the equation of tangent and normal lines to the curve xs sin(2y) = y cos(2x) at the ㅠ ㅠ point…

A: Solution of this question is

Q: An equation of the tangent line to the curve y = sin(x) at x = Зп /4 is %3D y = - (х — Зп /4) .

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

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

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Q: 1) Find the equation of the tangent line to the curve: x* + xy – y = 7 at (3,2) %3D

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Q: ind the slope of the tangent line to the curve y = V4x – 3 at the point (13, 7).

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

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Q: Find the equation of the tangent line to the curve y = xVĩ at the point (1, 1). y =

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Q: Determine the equation of the tangent line to the curve x- 2xy = 2y² +1 at the point (1:0).

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Q: Find the equation of the tangent line on the curve defined by 2xy- y² =1 at x = 1. A y=x-1 B y=1 ©…

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

A: Given curve is y=x. To find equation of tangent line at point 1,1. Differentiating the given curve…

Q: Show that the tangent lines to the curve y = (paisin x)/x at x = pai and x = -pai intersect at right…

A: y=π sinxx Differentiating with respect to x, we get dydx=ddxπ…

Q: Find a curve in the xy-plane that passes through the origin and for which the tangent at (x, y) has…

A: Tangent is the line that just touches the curve at a single point. Derivative of the curve at a…

Q: 2. Find the coordinates of the points on the curve y = r' - x² – x +1 where the tangent line is…

A: Solution:- step-by-step solution of above  question is given below.. The given curve is  y=x3-x2-x+1…

Q: B) Find the skpe of the Ine tangen to the curve y = sin-x at the poit

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Q: Calculate the equation of the tangent line to the curve 2x 3 + xy + 3x + y = 2 at the point (0, 2).

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Q: 2x2 y = Зх — 1

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Q: 2- Find the equation of the tangents to curve given parametrically by Y= sin(x²) + 1 at (x,y)= (…

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Q: Find the slope of the tangent line to the curve 2 sin(z) +4cos(y) –- 3 sin(z) cos(y) + z = 7x at the…

A: The objective is to find the slope of tangent line to the curve at the point (7π, 3π/2).

Q: Find the derivative of the parametric curve x=2+cost, y=1+sint at the point t=π3.

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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: The slope of the tangent line to the curve In(zy) = y² – 1 at the point (1, 1) is m =

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Q: The line that is normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) intersects the curve at what other…

A: Given thatx2 + 2xy – 3y2 = 0          …(1)On differentiating equation (1) with respect to x,

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

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Q: Find the point on the curve y = x³ + x2 – 1 where the tangent is perpendicular to the line y = -x

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

A: Given, curve and point

Q: Find the equation of the tangent line to the curve x = 1 - cose, y = 0 -sin0 at 0= 4 -

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Q: Find the equation of tangent line to curve x= t^(2)-2t and y=t^(2)+2t at the point t=2?

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Q: tangent

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Q: Calculate the equation of the tangent line to the curve x^2+xy+3x+2y-1=1 at the point (0,1)

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Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: