Find the length of the curve y=Arc sin e^x when y= pi/6 to y=pi/2

Q: Find the tangent line to the curve y = 2 tan (πx/4) at x = 1.

A: We first find y' at x=1 using chain rule

Q: Find the tangent line to the Curve t) =(sin 4), cos (t),+> at (0,l,0) क

A: We are given parameteric equation of curve .

Q: Find any points on the curve given by x = cos t, y = sin 2t, 0<t< 2n where the tangent is vertical.

A: The given parametric equations of curve are  x = cost y = sin2t To find the slope of the tangent,…

Q: The curve y = tan x crosses the line y = 2x between x = 0 and x = pai/2. Use Newton’s method to find…

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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 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 y = arcsin(e') at t= 0. II

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Q: Find the slope of the tangent line for the curve r = 4 – 5 cos 0 when 0 6 %3D -

A: r=4-5cosθ

Q: Find the slope of the tangent line for the curve r = 8 – 6 cos 0 when 0 4

A: Consider the provided curve, r=8-6cosθ where θ=π4. Find the slope of the curve. First we converting…

Q: Find the exact length of the curve  y = ln(sec(x)), 0 is less than/equal to x is less than/equal to…

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Q: Integrate cot(r) In(sin(x))dx.

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Q: Find an equation of the tangent line at the origin to the curve 1+ sin(x + y) = xy + cos y.

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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: If y =4 tanh x + sinh 2x, what is the slope of the curve when x = 2? Assume h = 0.5 and 0.01;…

A: The solution is given below

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: 3) Find the equation of the curve whose arclength from the point (4, 1) to the point (9, -1) is…

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Q: Find equations of the tangent and normal line to the curve y = x cos x at x = t/2.

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Q: find an equation of the tangent line at the point specified. y = sin x + 3 cos x, x = 0

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Q: Find the slope of the tangent line to the path of a carnival ridex=8 cos(t) + sin(81), y = 8 sin(t)…

A: The slope of the tangent is dydx.

Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x -dx, in six…

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Q: Find the equation of the tangent line to y = 14e cos(x) at x 0. %3D

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Q: find equation of tangent line and normal line to the curve y = tan(x) at      (pi/4, 1)

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Q: Find the equation of the line tangent to the graph of f at the indicated æ value. y = 4 sin¬1 2x, æ…

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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: The x-coordinate (measured in meters) increases at a steady 10 m/sec. So, dx/dt= 10A point on the…

Q: Find , if y = x sinh x - cosh x %3D dx

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Q: What is the slope of the line tangent to the curve x = 7et – sin 6t and y = 6e6t - cos 6t at the…

A: We have to solve given problem:

Q: Find the linear approximation to y=arcsinh(2x) at x=6.

A: Given:y=arcsinh(2x) and x0=6To find:The linear approximation to y=arcsinh(2x) at x0=6

Q: Find the slope of the tangent line to the curve 2xy + 4* = y2 – tan(2x) at the point (0, 1). Give…

A: Given curve:      2xy + 4x = y2 - tan2x   slope of the tangent line  =  ?

Q: Differentiate y= 3-carhx tespect to X 6+ Sinh x

A:

Q: Find an equation of the tangent line to the curve atthe given point.   y =sin(sin x) , (π , 0)

A: y = sin(sinx) dy/dx = cos(sinx).cosx

Q: 4. Find the equation of the tangent to h(x) = x´sin(2x) at x = 1 [no unit circle needed]

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Q: ) If y = cos2x + 2cosx for 0 < x < 2n. Find the points at which the tangent line is horizontal.

A: Given function is y=cos2x+2cosx for 0≤x≤2π. To find the points at which the tangent line is…

Q: Give the equation of the tangent line to the graph of 3sin y − ln(e sech x) = tan−1(x2y) + x/3 at…

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Q: Find the equation of Besan circle for y =ln(sinx) at x= 2.

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Q: Find the equation of the line tangent to the graph of y = arcsin (tanh(x)) at r = = 0.

A: we have to follow next step

Q: Given the velocity function v of an object moving along a line,explain how definite integrals can be…

A: From the given data:

Q: Find an equation of the tangent line to y = 5 sin(x) at x 4

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Q: Find an equalion of the tangent line to the curve at the given point. y= (1+x) cos x, Co, 1)

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Q: The length of one arch of the curve y = sin x is given by L = | VI + cos² x dx. 0, Estimate L by…

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Q: Find an equation of the tangent line to the curve atthe given point.y =sin ( sin x) ,…

A: Find an equation of the tangent line to the curve atthe given point.y =sin ( sin x) ,…

Q: (b) Find the equation of tangent and normal to the curve f (x) |2 – sin(2x) at x 4

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Q: Find the slope of the line tangent to the curve at the given point y%3D25 sin x; x = F/3

A: We find dy/dx

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

A:

Q: Find the equation.of tangent lin'e at x \ xT In Vx fCx) CS Scanned with CamScanner X= 1 %3D

A: Given: f(x)=x4 ln x3    at x=1

Q: Find an equation of the tangent line to the y = sec(x) – 6 cos(x), P = 3 y =

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Q: Find an equation of the tangent line to y = 7 tan(x) at x = 4

A: The given function is y=7 tan(x) at x=5π4

Q: Find an equation of the tangent line to y = f(x) arctan(x) at = V3. x =

A: We have to find equation of tangent line

Q: Find an equation of the tangent line to y = 9 sin(x) at x = *.

A:

Q: Find the values of x between 0 and π where the tangent line to the graph of y=sin⁡(x)cos⁡(x) is…

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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.