Textbook Problem The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30 seconds is shown. Estimate the distance traveled đuring this period. (km/h) 80 40 20 30 (seconds) 10

Q: The point on the curve y = 2-x nearest to (3,2) is (1,1) (0,2)

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Q: The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30…

A: The interval of the given graph is [0,30] Where a = 0 and b = 30 Here we have to use midpoint rule…

Q: 3. Sketch a graph of the position of an object that has an average velocity of • -5 mph for times…

A: As we know the rate of change of position  is velocity let object is moving in x direction hence…

Q: Find the orthogonal trajectories of the family of curves y^3 = 3(? − ?). Draw a few representative…

A: We will find out the required solution.

Q: Find the orthogonal trajectories of the family of curves. Sketch several members of each Family y =…

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 81x2…

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Q: if any. Find the absolute extremum point (s) of f(x) = el-cosa on [-, ],

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Q: Find the equation of the tangent line to the graph f(x) = 2x² + 5 at P(-1,7)

A: We will find out the required equation of tangent.

Q: An equation of the line tangent to the graph of f(x)= x(1-2x) at the point (1,-1) is

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Q: Find an equation of the tangent line to the graph at the given point. 3(x² + y2}² = 100(x? – y²),…

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Q: Find the length of the curve defined by 2? = 2y3 from x = 0 to x = 4:|| %3|

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Q: Find the equation of the tangent line to the graph of the function f (x) = /4x³ + 5 at the point…

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Q: Find the orthogonal trajectories for the family of curves x2 − 2y2 = C . Use a graphing utility to…

A: Concept: Trigonometry is used in finding distance and angles, there are six trigonometric ratios…

Q: Sketch the curve if y' is negative and y'' is negative on the interval of (-infinity, -3) with a…

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Q: 4) Determine an equation for the tangent to the graph of the curve y = (6x - 3)(-x? + 2) when x = 1.…

A: Note: To draw the tangent of a curve at a given point, first we have to find out the slope of the…

Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent.

A: Given that  f(x)=(-8x)/(√(2x-1))  The function has a horizontal tangent  To find the point at which…

Q: The slope of the tangent line to the curve at (x,y) point is defined by 3log3 (1- ) (k +1). If the…

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Q: Use the alternate definition, lim Ax)-Aa) to determine the instantaneous rate of X- a change of Ax)…

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Q: Find an equation of the tangent line to the parabola y=x2+x such that it passes through the point…

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Q: (8 points) Find the slope of the line tangent to the graph of 1 f (x) = 2x* – 32x + 17x2 – 9x + 4 at…

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Q: 2. Find the equation of the horizontal asympto

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Q: Find an equation of the tangent line to the parabola y − x2 - 8x + 9 at the point (3, -6).

A: The derivative of a curve at a point gives the slope of the tangent to the curve. It can be…

Q: Find the equation of the tangent line to the graph of y = 2x - (4 / √x) at the point (4, 6).

A: Given,            y = 2x - 4x and Point is 4, 6

Q: The slope of the tangent line to the graph of the function y = 7Vx – 3 at (9, 18) is - O 3 - 2.00 O…

A: Simply take the derivative of the function at that point.

Q: Find the equation for the perpendicular trajectories of the family. 1. x - curve

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Q: Find an equation of the tangent line to the graph of f(x)=x^2+3x-7 at the point (1,-3)

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Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

Q: Find an equation of the tangent line to the parabola y=x2  -8x+9 at the point (3, -6)

A: Given :          y= x2-8x+9

Q: find the critical points and determine whether they are minima, maxima, or neither g(θ) = sin2 θ + θ

A: For critical points, Equate the derivative of the function to 0. Here, g(θ)=sin2 θ+ θ

Q: 2Xin 2. O dy/dx if

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Q: Which hyperbolic functions are increasing on their domains?

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

Q: y = In(x-2) ex+1

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Q: At whhat point on the parabola y = x - 3x-5 is the tangent line parallel to 3x-y 2

A: Given y=x2-3x-5 To find the tangent line parallel to 3x-y=2

Q: Find an equation of the tangent line to the graph of the function f(x) = 2x² - 4x +5 at the point…

A: Given, f(x)=2x2-4x+5

Q: Find the point on the parabola y= -X-+4 whose tangent line is parallel with y= 3x-5,

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Q: The tail ends are extended indefinitely in both sides, but do not meet the x-axis, although they get…

A: As per our guidelines we are supposed to answer only one question per post so I am solving first…

Q: Find an equation for the tangent line to the curve n = 4- 2 at (-1,3).

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Q: 7. Find the equation of a line tangent to the graph of f(x) = cotx at x = π/4. Show all steps to…

A: Given :fx=cotx

Q: The slope of the tangent line to the parabola y = 3r2 + 6x + 2 at the point ( – 2, 2) is: The…

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Q: Find the equation of the tangent line to the graph of f(x) = x² – 4 at the point (3, 5). -

A: The equation of the line passing through the point (x1,y1) having slope m is given as (y-y1)…

Q: Find the equation of the line tangent to the graph f(x) = – at the point (4,1).

A: Given:            fx=4x To find the slope of the tangent line, find the value of the derivative of…

Q: A pole 8 meters long is carried horizontally along a corridor 3 meters wide and into a second…

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Q: Find an equation of the tangent line to the graph of y = f(x) when x = 2 if f(2) = -6 and f'(2)= 5.…

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Q: Find the directions in which the function increases and decreases most rapidly at Po-

A: Given, fx,y,z=4lnxy+lnyz+lnxz, P01,1,1 Direction in which function f increases is given by, u^=∇f∇f,…

Q: What point on the curve y = x is closest to the point (5, 0)?

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Q: Determine an equation for the tangent to the curve f(x) = 2x3 + 6x2 - 2  at x = -3

A: Given query is to find the equation of the tangent.

Q: Find an equation of the tangent line to the graph at the given point.

A: Given: 3 x2+y22 = 100 x2 - y2  and the point (4, 2) To find: An equation of the tangent line to the…

Q: 3. If the graph of y=fcx) has a horizontal tangent at x=a, what is happening at this point ? I…

A: For a function ; a point is considered. A horizontal tangent exists at this point which means that…

Q: the equation of the tangent line to the graph of f(x) = 4x3 + 7x² - 8x – 6 at x = -1.

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Q: 4. Use your figure to study the sign of vr(t) in the time interval [-4 : 4]. Does vr(t) have any…

A: Given voltage potential v(t) is, vt=0.250t4+0.166t3-0.500t2                   .......1 and the…