A pole 8 meters long is carried horizontally along a corridor 3 meters wide and into a second corridor at right angles to the first. What must be the minimum width of the second corridor in meters? (Hint: This is a maxima-minima problem making use of derivatives of trigonometric functions.)

Q: At which points on the curve y = 1+40x3 – 3x does the tangent line have a locally maximum slope? A…

A: Solve the following

Q: Find the slope of the tangent line. y = cos3x at x= -5pie/12

A: Given:     y = cos3x      At x = -5π/12

Q: Find the equation of the tangent line to the graph of f(x) = 2x² –In Vx at X = 1. %3D

A: First we differentiate to find the slope then use formula to find the equation

Q: Please show step-by-step solution!

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Q: The tangent line to the graph of y = g(x) at the point (1, 4) passes through the point (2, 3). Find…

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Q: Find the equation of the tangent line to the function h(x) = xv4 + 2x at x = 6. %3D %3D

A: Differentiate the function with respect to x to find the slope of the tangent line.…

Q: The slope of the tangent line to the graph of f(x) D x2 at a = -1 is: %3D %3D

A: Given  equation of the graph  f(x) = xx2-x                        ...........(1) We have to find the…

Q: Find the maximum possible error in the computed value of the hyperbolic sine function, sinhx = at…

A: Solution

Q: he tangent line to y = f(1) at (-3,9) passes through the point (9,-3). Compute the following.

A: The slope of the line passing through the points, (x1,y1) and (x2,y2) is given by .

Q: 4. Find the equation of the tangent line to the graph of g(x) = v2-x at x =-7 %3D

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Q: pG)= sinh! (tan 3x

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Q: Give one problem for hyperbolic differentiation

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Q: Find an equation of the tangent line to f (x) = x² Vx4 – 12 at x = 2. - %3D

A: Explained below

Q: The ends of a 300 metre length of string are to be fixed to a wall at points A and B to form a…

A: The ends of a 300 metre length of string are to be fixed to a wall at points A and B to form a…

Q: Find the equation of the tangent line to the function f(x) = -3x2 – 2x at the point where x form y =…

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Q: If tanh x = 12/13  find the values of the other hyperbolic functions at x

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Q: do you agree that cubic function must have at least 1 x - intercept but not more than 3 whereas…

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Q: Find the equation of the tangent plane to z at (-4,2).

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Q: Find the orthogonal trajectories of the given family of curves: Circles through the origin with…

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Q: Find the equation of the tangent line to the graph of the function f(x) = v2x² + 1 at the point…

A: Given that: f(x)=2x2+1        at point (2, 3)

Q: Find the equation of the tangent line to the graph of f(x)= 1 at the point (2,1). %3D X-1

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Q: Determine the equation of a sine function with a minimum at and a maximum 57 at

A: Given minimum value at π3,-10 maximum value at 5π6,-2 To find: Equation of sine function General…

Q: Can you clarify the first part again, does it mean that the relative maximum, minima, and horizontal…

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Q: In the definition of hyperbolic functions, sinh (z) is equivalent to

A: The solution is written in step2.

Q: Show that no point on the graph of x 2 - 3xy + y 2 = 1 has a horizontal tangent line.

A: Given  x 2 - 3xy + y 2 = 1

Q: What is the isogonal trajectories family of curves x² - y² = a which intersects at an angle of ∅ =…

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Q: At 6:00 am, ship A is 200 km west of port, heading east at 25 km/h. At the same time, ship B is…

A: Given:  At 6:00 am, ship A is 200 km west of Port, heading east at 25 km/hr.and at the same time,…

Q: Which hyperbolic functions are increasing on their domains?

A: First of all, consider all the six trigonometric hyperbolic functions and their domains.

Q: ) Find the equation of the tangent f (x) = 4x - 8/x at a = 16. %3D %3D

A: Given: fx=4x-8x at x=16 For finding equation of tangent at x=16, we need to find y-coordinate for…

Q: Does Newton’s Method fail when the initial guess is a relative maximum of f ? Explain.

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Q: Find an equation of the tangent line to the graph of the function                         y = 4x…

A: The given equation is y=4xarccosx-1.   Find the slope of the tangent line by differentiating the…

Q: Find the equation of the tangent line to f(x) = 8x² – 5x – 40 at (3,17). %3D

A: Solution of the problem as follows

Q: Find the orthogonal trajectories to the family of curves:

A: Consider the given equation. x2=C-12y2lny2-1 Find the derivative of the function with respect to x.…

Q: Find the slope of the tangent line to the graph at the given point. 4xcosy +1 = 5 at the point (2,)

A: Solve, as follows: 4xcosy+1=541cosy+x-sinydydx=0dydx=cosyxsiny

Q: Find the asymptotes of the hyperbolic tangentf(x)=tanhx.

A: We first simplify tanh(x)

Q: Find the equation of the tangent f (x) = 4x – 8/x at a = 16 %3D

A: Equation of line with slope m and passes through point (xo , yo) is (y-yo) = m(x-xo)

Q: The tangent line to y=f(x) at (1,-3) passes through the point (3,9). Compute the following: f(1)=?…

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Q: Vehicle A is headed due west from a fixed point P at a rate of 45 miles/hour. Vehicle B is headed…

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Q: At which points on the curve y = 1+40x³ –3x does the tangent line have a locally naximum slope? A…

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Q: The ________ of a sine or cosine curve represents half the distance between the maximum and…

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Q: Express the length l of a chord of a circle of radius 8 as a function of its distance x from the…

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Q: cosh

A: Given function is Fx=cosh1x3.

Q: Find an equation of the tangent line to the graph of the function (x)= Vx –7 at the point (23, 4).

A:

Q: Did you know that out from the rotation of a Ferris wheel a graph of either sine or cosine…

A: Here, x-axis represents the time in minute and y-axis represents the height in meter.

Q: Differentiate the following hyperbolic functions.

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Q: Find the tangent line to ƒ (x) = (2 – 4x²)° at z = 1. %3D

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Q: Kappa Curve: x²y² + y* = 2x² %3D

A: We are asked to find the slope of the tangent line at the given point