Use the guidelines of this section to sketch the curve   y = x (x- 4 )3

Q: Use the guidelines of this section to sketch the curve   y =  x - 3x 1/3

A: Let us make a table for the function x -8 -1 0 1 8 y -2 2 0 -2 2

Q: Use the guidelines of this section to sketch the curve.   y = x/ x-1

A: To find the x-intercept we plug y=0 So x-intercept is 0 To find the x-intercept we plug x=0 So…

Q: Use the guidelines of this section to sketch the curve. x2 - 25 y = x2 - 5x

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Q: Sketch the curve f(x) = x/(x-1)^2. Show complete solution

A: We have to sketch the given curve f(x) = x/(x-1)2. To sktech the given curve we will follow the…

Q: Write the equations of the lines tangent to the curve y x- 4x at both a 0 and a 2. Then, determine…

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Q: Use the guidelines to sketch the curve  y = 2 x2  / ( x 2  -1 )

A: For, x=0, y=0  So, the y-intercept is 0   Then we plug y=0 and find x so, x-intercept is 0.

Q: Use the guidelines of this section to sketch the curve. x - 5

A: Given : Function y = xx-5 To find : Graph of the given function?

Q: Use the guidelines of this section to sketch the curve   y =x ln x

A: We can not have a negative number inside log, so x>0 This is the domain of the function.  We will…

Q: Use the guidelines of this section to sketch the curve   y =x/  sqrt( x2   +1)

A: This function can not have the denominator equal to 0, so there will be no vertical asymptote.

Q: Use the guidelines of this section to sketch the curve.   y = 2√ x    -x

A: We will make a table for the function  x 0 1 4 9 y 0 1 0 -3

Q: Find the exact length of the curve = √(y - 3), 1 ≤ y ≤

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Q: Use the guidelines of this section to sketch the curve   y =x / ( x3  -1 )

A: Given: To sketch the given curve using the guidelines.

Q: Use the guidelines of this section to sketch the curve  y =   x4  -4x

A: We have given the curve; y =   x4  -4x

Q: Find the point on the curve y2 = ;(x+1) which is nearest the origin.

A: We have to find the point on the curve y2=52x+1 which is nearest the origin.

Q: Find the equation of the tangent to the curve  y = -5x2 + 6x +7 at the point (1/2 , 35/4)

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Q: the guidelines of this section to sketch the curve: y = x+ – 8x

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Q: Use the guidelines of this section to sketch the curve.   y = x/ x2-9

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Q: Use the guidelines of curve sketching to sketch the curve y = 1-x2 %3D

A: Given: y=x1-x2

Q: Use the guidelines of this section to sketch the curve.   y =  x4 - 4x

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Q: Use the guidelines of this section to sketch the curve.   y = (4 - x2)5

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Q: Write the equation of the tangent line to the curve (a lemniscate) 2(x2 + y²)“ = 25(x² – y²) at the…

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Q: Use the guidelines of this section to sketch the curve   y =2 sqrt x - x

A: Given              y=2x-x

Q: Use the guidelines of this section to sketch the curve.   y= 3√(x3 + 1)

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Q: Find the point on the curve y2 =;(x + 1) which is nearest the origin.

A: If (x, y) is any point on the curve nearest the origin then the square of its distance from the…

Q: Find an equation for a line that is tangent to the graph of y = ex andgoes through the origin.

A: To find the equation of a line that is tangent to the graph of y=ex and passing through origin.…

Q: Use the guidelines of this section to sketch the curve   y =2 x- tan x  ,  - pie/2<x <pie /2

A: Given: Differentiate the above expression and equate to zero to find the local minima and local…

Q: Use the guidelines of this section to sketch the curve.   y = 2 + 3x2 - x3

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Q: Use the guidelines of this section to sketch the curve. х — 6 y = x2

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Q: Use the guidelines of this section to sketch the curve.   y= 3√(x2  -1)

A: We need to find the x intercept, y intercept, vertical asymptotes, horizontal asymptote etc to…

Q: Use the guidelines of this section to sketch the curve   y = x e -1/x

A: The given function is y=xe-1x. Sketch the graph of the above function as shown below.

Q: Use the guidelines of this section to sketch the curve.   y = 1/ x2 -9

A: Let us plot a table with values of x and y. x y 0 -8 1 -8 -1 -10 2 8.75

Q: Use the guidelines of this section to sketch the curve.   y = x √(5- x)

A: We can not have negative number inside square root So, 5-x≥0 x≤5  Let us make a table of values x…

Q: Use the guidelines of this section to sketch the curve.   y = x 5   - 5x

A: We make a table with different values of x and y.  x y  0 0 1 -4 -1 4

Q: Sketch the curve y = x/(x² – 9). Enumerate the steps in your solution.

A: as per our guidelines, we are supposed to answer only one question if there are multiple questions…

Q: Find the closest point to the point (2,0) on the y = x curve.

A: To find the closest point to the point (2,0) on curve y=x

Q: Use the guidelines of this section to sketch the curve.   y = x2/ x2+ 9

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Q: Find a point on the curve y = x2 that is closest to the point (18; 0)

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Q: The curve is given by 2 + 1), 0<x<3. 3

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Q: Use the guideline of this section to sketch the curve 1. y = 1 + 1/x + 1/(x ^ 2)

A: To Sketch: y=1+1x+1x2 Explanation: (a). Domain and Range y=1+1x+1x2is defined everywhere except…

Q: Find the x-coordinate of the point where the curve y = x3 - x crosses the horizontal line y = 1.

A: Given:                                 y=x3-x and y=1  Let                                y=x3-x…

Q: Sketch the curves 1.) y = 3+4x-x2

A: the equation of the curve is: y=3+4x-x2 we have to sketch the given curve.

Q: 2x at x =1 y = Зх-1

A: Find dydx as follows. y=2x23x-1dydx=22x3x-1-3x23x-12dydx=23x2-2x3x-12 Find dydx at x=1 as follows.…

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x

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Q: Use the guidelines of this section to sketch the curve   y = x e -x

A: Consider the given function as y=xe-x

Q: Find the point on the curve y = 3x + 4 which is closest to the point (5, 0). Preview Preview

A: Let (x, y) be the point closest to the point (5, 0) We will calculate the distance between these two…

Q: Use the guidelines of this section to sketch the curve. y = x/7 - x2

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Q: Use the guidelines to sketch the curve; y= x/sqrt x^2+1

A: To sketch the curve y=xx2+1

Q: or the curve y = ax³ + bx² + 12x - 7, what values of a and b will make the tangents to the curve at

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.