If, as x→-0 or as x0, the values of R(x) approach some fixed number L, then the line y = L is a of the graph of R.

Q: What will be the axis of symmetry, the line about which a figure or curve is upon itself, between…

A: Given :   y=4x-2

Q: What is the families of the curve of all straight lines through the fixed point (h,k).

A: The differential equation representing the families of curve of all straight lines through the fixed…

Q: Given that f(7) = 9 and f'(7) = -3, find an equation of the tangent line to the graph of y = f(x) at…

A: Given that f(7) = 9 and f'(7) = -3. Here, the points x,y=7,9 and the slope is m= - 3. Note that, the…

Q: In the function f(x) = a(x + 2)(x – 3)%, a and b are both integer constants and b is positive. If…

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Q: Find the line L, that passes through the point P(1,2) and parallel to the line L2: x+2y=3.

A: Given data is: The equation of the line L2: x+2y=3 To find the equation of the line L1 that passes…

Q: If, as x→-0 or as x→0, the values of R(x) approach some fixed number L, then the line y = L is a of…

A: If as x→-∞ or x→∞, the values of R(x) approach some fixed number L, then the line y = L is a…

Q: Let  f(x)=1/2x^2-1.  Find the slope  of the secant line that contains points P=(2,f(2)) and…

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Q: Determine whether there exists a constant c such that the line x + cy = 1: passes through (3, 1).

A: We have to determine the value of constant c such that the line x+cy=1 is passing through the point…

Q: Suppose the slope of the curve y = f'(x) at (4, 7) is §. Find f'(7).

A: Given slope of the curve y=f-1(x) at (4,7) is 45

Q: Find the shortest distance between the point A (3, 10) and the line y = x + 1.

A: Our Aim is to find the shortest distance between the point A(3,10) and the line y=12x+1 -(i)

Q: For what value of k will the line kx + 5y = 2k be perpendicular to the line 2x - 3y = 1?

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Q: Find the formula for the level curve of Cobb-Douglas: f (L, K) = L'/4K³/4 = 8 in the form K = g (L).…

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Q: If the lines joining origin to the points of intersection of the line fx - gy = 2 and the curve x²…

A: Though it is analytical geometry problem but it is a B.SC problem, more than high secondary…

Q: The line in R that is parallel to the y-axis and passes through the point (1, 2, 3) has equation + t…

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Q: By experimentation, determine the approximate value of a (where 3 < a < 4) at which the graph…

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Q: For the graph of the linear function f(x) = mx + b, m is the  _____ and b is the _______ .

A: For the graph of the linear function fx=mx+b, m is the  _____ and b is the _____.

Q: If, as x→-∞ or as x-→∞, the values of R(x) approach some fixed number L, then the line y = L is a of…

A: If , as x→-∞ or as x→∞, the values of Rx approach some fixed number L, then the line y=L is a…

Q: Suppose (P, Q) is the point on the graph of y=/x closest to (1, 0). What is the value of P+ Q?

A: Let's find.

Q: Sketch the graph of the level curve corresponding to z = 6 for the following function. z = f(x,…

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Q: Match the following relations to their graphs. avy=z³-4r bv y = 91³- - I cvy=z³-4z² y = 21² al |> 13…

A: To match the given relations to  their graphs we first try to find the roots of the given…

Q: If a line intersects the x-axis at 'r' and the y-axis at '1/r', at what point (x,y) does it…

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Q: 6. If, as x-- or as x- 0, the values of R(x) approach some fixed number L, then the line y = L is of…

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Q: What is the length of the graph of y = In(x<+1) - x from x = 0 to x = 3?

A: Given  The graph equation is y=lnx2+1-x  from  x=0 to x= 3 .   Formula :- Arc length of curve…

Q: The line y=-Lx+8 has perpendicular whrich is fangent to the graph of Find the value of ke y = (x²2)…

A: Explanation of the answer is as follows

Q: If, as x approaches some number c, the values of |R(x)|→∞, then the line x = cis a of the graph of…

A: If, as x approaches some number c, the values of R(x)→∞, then theline x=c is a ..................of…

Q: Suppose that P is twice as far from (0, 0) as P is from (6, 0 Find such a point on the x-axis.

A: Let A0,0 and B6,0. It is given that P is twice as far from A0,0 as from B6,0. We know that if point…

Q: Find a relationship between x and y such that (x, y) is equidistant the same distance from the two…

A: Given points are: 4,-1 and -2,3 The distance between the points 4,-1 and x,y is: d1=x-42+y+12 The…

Q: Given that f(−2)=−8f(−2)=−8 and f′(−2)=−7f′(−2)=−7, find an equation for the tangent line to the…

A: Given : f(-2) = -8, f'(-2) = -7   To find the equation of the tangent line to the graph of y= f(x)…

Q: fird the equation of the fangent lineto the graph of Y= ☆ at X=2

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Q: Determine the value(s) of k such that the lines 2y= -kx +6 and 3y-x= 2kx+3 have the same…

A: The given line equations are 2y=-kx+6 and 3y-x=2kx+3. Rewrite the equations as shown below.…

Q: Addison and Kelsey are running on a path modeled by x² + y²-14x-16y-2870, where the distance is in…

A: Follow the procedure given below.

Q: Show that the graph of y = 5 and y = log,. x are reflections of each other with respect to the line…

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Q: Determine the point(s) at which ƒ(x) = x3 - 12x has a horizontaltangent line

A: The points where the tangents are horizontal are the points at which slope is zero.That means,…

Q: If, as x approaches some number c, the values ofR1x2 S q, then the line x = c is a of the graph of…

A: Given,   If, as x approaches some number c, the values of |R(x)|→  ∞, then the line x = c is a…

Q: The line y = kr + 4, where k is a constant, is graphed in the xy-plane. If the line contains the…

A: Given line is: y = kx + 4 ................... (1) The line contains the point (c, d). Then (c, d)…

Q: Find the slope intercept form of the line satisfying the given conditions. parallel to 4x+16y=23.…

A: The line parallel to the given line 4x+16y=23 should have the same slope as the given line.

Q: [a] Find the shortest distance from the point (2, -1, 4) to the straight line x = 2, y = 3+tand z =…

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Q: If f(x)=3x^2-2, and g(x)=f−1(x), what is the slope of the curve g(x)=f−1(x) at the point (10, 2)

A: Given f(x) =3x²-2  And g(x)=1-f(x) =1-(3x²-2) =1-3x²+2 g(x)=-3x²+3 For slope of curve g(x)…

Q: On weekends and holidays, an emergency plumbing repair service charges $60 for the first 30 minute…

A: According to the problem, we need to plot the graph of the function C(x) for 0&lt;x&lt;=90. So, 1st…

Q: Show that the graph of y = 3* and y = log,x are reflections of each other with respect to the line y…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the relation between x and y such that the point (x,y) is equidistant from the points (7,1) and…

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Q: Consider the following. 2 X- 3 x² - 3 x (a) Find the points of intersection of the curves. (x, y) -…

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Q: an object is traveling on a path of y=sprt(x+3) where will the object be closest to (2,0)

A: We have to find the closet point to (2, 0)

Q: on the line ye -2x +8 that 1-) Find the point IS Close't to the onigin.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: (1) ( ) Find the shortest distance between two lines given x +2 -8 y = and y 2

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Q: The graph of a function y = f(x) in the xy-plane is the set of all points _______ that satisfy the…

A: Given: The graph of a function y = f(x) in the xy-plane is the set of all points _______ that…

Q: Show that the equation of the line in R' through distinct points (1, Y1) and (x2, Y2) can be written…

A: We have to show that the equation of the line in R2 through distinct points x1,y1 and x2,y2 can be…