In the function:  f(x)= (4x^2)/((x^2)+4)  When is the function in concave up and concave down using internal notation?  What are the inflection points of the function?  What are the vertical asymptotes?

Q: What are the three cases we must consider for finding horizontal/slant asymptotes?

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Q: Use limits to determine the equations for all horizontal asymptote.  y = (sqrt(x2+9)/(sqrt(9 x2+1))

A: The given function is

Q: 2x-5 lim 3-5x+x² I3D

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Q: Calculate limit of (square root of x^3-1)-x^2 as x approach to positive infinity. Thank you!

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Q: Illustrates how can a curve cross one of its horizontal asymptotes many times?

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Q: Find the asymptotes, intervals of increase, decrease, concave upward, concave downward, local max,…

A: No asymptotes, Increasing when X<3/4 Decreasing when 3/4<X<1 Concave down for x<1 Local…

Q: Use limits to determine the equations for all horizontal asymptote.  y = sqrt(x2+4)/( x)

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Q: Find limx->∞,if for all x>5

A: We apply limx->∞ on all sides.

Q: What is asymptots and how we will solve asymptots?

A: Asymptotes are the lines that curves approaches, as it tends towards infinity. There are different…

Q: Use a tble of functional values to evaluate: lim 12 z-2

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Q: find domain and asymptotes of  fx= x^2+x-2 over x^2-2

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Q: Estimate the horizontal asymptote of the function   by graphing f  for -10  ≤x ≤ 10. Then calculate…

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Q: What is Oblique Asymptotes?

A: Oblique Asymptotes also known as the Slant Asymptotes. It is represented along a line y=mx+b, where…

Q: The limit of the function as x approaches 1 from the left is ... (0/1 Point) 6- 4- 2 -10 -5 5 10 -2-…

A: Given-  To Find- The value of the limit of the function as x approches 1 from the left hand limit.

Q: Find the derivative of the function by the limit process. f(x) = x² + x - 5 f'(x) =| 4x – 8

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Q: Find the Limit (sin3x)/(5x^3-4x)

A: Obtain the limit value as follows.

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 the limit. Use a graphing utility to verify your result.

A: We need to find the following limit: We will use the following property of limit in this question:…

Q: Use limits to determine the equations for all horizontal asymptote.  y = (1 - x2)/( x2 + 1)

A: To find the horizontal asymptote using limit we find the limit of y when x approaches infinity.…

Q: Does local extrenum of x(sqrt(4))- x^2 exist?

A: Given function is: f(x) = x . {sqrt (4)} - x^2 f(x) = 2x - x^2 ; [consider the positive value of…

Q: lim (4x – V16x² + 3x – 5 (4* Зх — 5 00-x

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Q: Find the points on the graph of f(x) = 6x – 2x³ where the tangent line is horizontal. (Use symbolic…

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Q: Find horizontal asymptotes by showing limits for x → ∞, x → -∞. Give some argument (numerical or…

A: find limit for

Q: limit as x approaches infinity, 10x^5+x^4+31/x^6

A: Here an expression is x is given to us and we need to calculate the value of expression when x tends…

Q: 2- -2 -2

A: Asymptote : An asymptote is a line that a curve approaches, as it heads towards infinity.   The…

Q: write down a function with a horizontal asymptote and and reaches the value of that asymptote…

A: f(x)=cosx/x+1 is the required function.

Q: Consider lim3 x2 9 Find a maximum value of 6 such that x2 90.005 if |x - 3| < 6 (Use decimal…

A: We remove absolute value of |x^2-9|&lt;0.005 and solve for x.

Q: Find lim *2 x -2 In(x- 1) by using the La'Hospital Rule.

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Q: Estimate the limit numerically to two decimal places or state that the limit does not exist.

A: limx→23x−95x−25 Since we have an indeterminate form of type 00 Apply the L' Hospital's rule:…

Q: How to find  lim 4-x/x+3 while its approaching 3 from the left side.

A: we have to find limit value as x approaches to 3 from left side.

Q: correspondig limit x' +x -8x-12 a) lím x* +4x' +5x + 4x +4

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Q: 3) lim (x² + 1) X--1

A: Limit is a basic concept of calculus  which shows the behaviour of a function  when it tends to that…

Q: By using intermediate value theorem locate a root for the f(x) = 2x3 - 3x2 - 6.

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Q: 3) Find the vertical asymptotes (verify with limits) 2 x² - 4 f(x) =

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Q: Find thu constant a such that the function 15 Continuous on thi entire real line. Usinx gex)= a-7x…

A: Here we use the concept of limit

Q: Create a table of value (use 8 values - 4 on the left and 4 on the right) and a calculator to the…

A: Given problem:- Evaluate limx→610-x-4x+6by using 8 values table 4 left and 4 right

Q: Find vertical and horiztonal asymptotes for r(x)=8x^3/x^3+2x^2+8x

A: We generate vertical asymptotes  by the zeros of denominator ,so set denominator equal to zero as…

Q: Find  lim x+8/x-1 as x approaches -2 approaches

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Q: on the graph of f(x) = 54x - 2x3 where the tangent line is horizontal Find the points (Use symbolic…

A: Given,

Q: Use limits to determine the equations for all horizontal asymptote.  y = (sqrt(x)+4)/(sqrt( x+4))

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Q: Find the limit. Enter the exact answer. If the limit does not exist, indicate that using the check…

A: limx→∞sin-14x6-8x=sin-1limx→∞4x6-8x=sin-1limx→∞4xx6-8xx , [divide both numerator and denominator by…

Q: Find the limit. 28x-7x lim x4 x→4 2-x 2. 28x- 7x lim 日 x→4 2- Vx (Type an integer or a simplified…

A: The solution are next step..

Q: A quadratic function is given f(x) 2x^2 + x - 6. Express in standard from. Find vertex and x-and y…

A: We compare the given equation with y=ax2+bx+c So, a=2, b=1 , c=-6 At vertex : For x=-0.25 we find…

Q: Find the limit. x-x lim x→11- Vx х-х* lim x→11- Vx (Type an integer or a simplified fraction.)

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Q: Find the points on the graph of f(x)=3x-x^3 where the tangent line is horizontal.  (Use symbolic…

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Q: Find the limit of  limitx->0[(4-sqrt(16+x))/x]

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Q: Find the asymptotes, intervals of increase, decrease, concave upward, concave downward, local max,…

A: f(x)=x+1-xf'(x)=1-121-xfor increasing ,f'(x)≥0⇒1-121-x≥0⇒121-x≤1⇒1-x≥12⇒1-x≥14⇒x≤34intervals for…

Q: Find limit of x approaching 3: f(x) = x2-2x-3/(x3-5x2+7x-3)

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Q: Estimate lim 16 4 is approaching to using a table of functional values.

A: We will use the L. Hopital's rule to find the limit of the given function. to find limx→ 4(16x-4x-4)