For a given m, what are the largest values the slopes of thecurves y = sin mx and y = -sin (x/m) can ever have? Givereasons for your answer.

Q: If the normal to the curve y=f (x) at the point(3,4) makes an angle of 3/4pi with the positive…

A: Near the point of tangency, say (x0, y0), the slope f'(x) of the curve f(x) is approximately equal…

Q: 134 Find the slope of the tangent line to the graph at the given point. Cissoid: 4y2 – xy2 = x³ %3D…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: For x^2 tan(y)+6x=12 Find the equation of the tangent line at (2,0) and find the equation of the…

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Q: 8. Find the equation of the line tangent to the graph of y tan (sin) when z= V2/2.

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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: 9. Find the slope of the tangent line to the graph of f (x) = sin (cos 2x) at x = 1 A. -2(sin 2)(cos…

A: we have to find the slope of the tangent line to the graph of fx=sincos 2x at x=1

Q: Solve the following. 1. Find the tangent and normal line to Y = Vx2 + 9 at (4, 5).

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: Find the question of the that is tangent to the curve y=-3 cos2x at x= n/6. Express with exact…

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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: 4.1. Find the slope of the line tangent to r = 4 – 3 sin 0 for 0 = ™

A: The given question is based on the tangent and normal topic in which we have to find only the…

Q: A curve is defined by y=(1/3)sin(2x+1). Evaluate the angle between the tangent to the curve at x=2,…

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Q: Find the exact length of the curve. y = Vx - x2 + sin

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: Corresponding to θ=0, the x and y coordinates will be,

Q: Find the slope of the tangent line to the given curve at the point corresponding to the specified…

A: Solve by converting polar form into coordinate form

Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+2…

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

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Q: Find the equation of the line tangent to the graph of f(x) = -2 sin (x) – 1 at x = 4. %3D (Enter an…

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Q: Use linear approximation, i.e. the tangent line, to approximate 3.7° as follows: Let f(x) = x°. The…

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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: [x € [0,x] T: sinx + cos (2y) = 1, y E 4: 4

A: Given equation of graph is sinx+cos2y=1 The slope of a graph at a point is given by the derivative…

Q: What is the slope of the line tangent to the curve x = 9e' – sin 8t and y = 3e8t - cos 8t at the…

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Q: At what point on the interval (0, 7/2) does the tangent line to the curve = 3x + V3 cos x – sinx…

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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: At the given point, find the slope of the curve or the line that is tangent to the curve, as…

A: Use derivative

Q: 12. In which of the following methods, we approximate the curve of solution by the tangent in each…

A: In Newton's Method , we approximate the curve of solution by the tangent in each interval .

Q: 1. Use four equal-length Hermite curves to interpolate y = sin(x) in the interval [0, 2r].

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Q: Find the equation of the curve which passes through (1,8) and at any point (x.y) on th curve the…

A: To find: Equation of curve which passes through (1,8) and at point (x,y) the tangent line has slope=…

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: 1. If f(x) = (2x)cosx, then f'(x) =?

A: Dear student as per our rule in one session we can only solve one question please post the other…

Q: Find a point of the following curve at which the tangent line has equation = x + T. .2 2.xy –…

A: Given equation of tangent  is     y=x+π⇒ slope of tangent  =1

Q: 6. P=(0,9) Sin(x)+ Cos (x)

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Q: Suppose the slope of the tangent line at any point on a curve is x+4yz. If the curve passes thru…

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Q: Find the x-value(s) at which the tangent line to the curve y=(6x+1)/(ex) is horizontal. If there are…

A: Here, we need to find the x-value(s) at which the tangent line to the curve y=(6x+1)/(ex) is…

Q: Suppose the tangent line to the curve  y= f(x) at the point (2,5)has the equation y= 9-2x. If…

A: Given: The equation of the tangent line to the curve y= f(x) at the point (2,5) is y= 9-2x. Newton’s…

Q: 1. If Y= 4 cos x + sin 2x, what is the slope of the curve when x=2.

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Q: Find the equation of the tangent line of y = 9e* at xo = 0. (Use symbolic notation and fractions…

A: The given function is:y=9exThe point is x0=0

Q: 41. Find the points on the graph of f(x) = 5- 2 sin.x, 0<x 27, at which the tangent line is parallel…

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Q: For which x-value(s) is the tangent line to the curve y=tan x parallel to the line y=2x ? Select all…

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Q: For what values of x does the graph of f(x) = 3e*cosx have a horizontal tangent line? 4.

A: Explanation of the answer is as follows

Q: 7. Find all x-coordinates where the tangent line to y = f(x) = sin(2x) – cos?(2x) is horizontal. -

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Q: Find an equation of the tangent line to the graph sin(x) + y² = 4 at (π, 2).

A: This question can be solved using the concept of tangent and normal.

Q: Use linear approximation, i.e. the tangent line, to approximate √16.4 as follows: Let f(x)=√x. Find…

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Q: 4. Find the slope of the tangent line to r = cos 0 at 0 = 3 %3D

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Q: 1. Given y = sin(x In.x), what is the slope of the tangent line at (e, 0)? (The red line.) 2. Given…

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Q: Find the exact length of the curve. y = √(x - x2) + Sin-1 √x

A: Given curve is y=x-x2+sin-1x.

Q: ) Find the equation of the tangent line to the curve y = 2x cos x at the point (π,-2π). The equation…

A: we have to find tangent to f(c) at x=pi

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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Q: At what value of x does the curve 1„2 sin y = 3y +x² + 4x have a horizontal tangent? (Supporting…

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