Sketch a graph of the function y = 1/3x^3 + 2x^2 + 3x How can we find the horizontal and vertical asymptotes? How can we find the local maximums and minimums? How do we find inflection points?

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 asymptotes.

A: Use the limit  y=x2+99x2+1  =x2(1+9x2)x2(9+1x2)  =1+9x29+1x2

Q: Identify the labeled x-coordinate on the graph at the right as the location of an absolute minimum,…

A: Given:

Q: ate a continous and differentiable functiin f(x) with the following properties:  f(x) is decreasing…

A: It is given that , f(x) is decreasing at x=-6, f'-6<0 f(x) has a local minimum at x= -3  and f(x)…

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

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

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Q: The graph of f(x) = 5(x – 1)2 – 6 is a parabola that opens --Select--- , with its vertex at (x, y) =…

A: Given equation  f(x) =5x-12-6

Q: solar oven is to be made from an open box with reflective sides. Each box is made from a 30 in by 18…

A: Given. Cuboid is formed from a square sheet of dimension 30 inch cross 18 inch. To calculate the…

Q: Sketch the graph of g(x), identify the absolute maximum, the absolute minimum, the local maximum and…

A: the given function is: we have to sketch the graph of the function g(x). then we have to identify…

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

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Q: Estimate and classify the critical points for the graph of the function. 4. -4 2

A: A critical point of a function of a single real variable, f(x), is a value x0 in the domain of f…

Q: Explain the difference between an absolute maximum and a  local maximum. Illustrate with a sketch.

A: given,       absolute maximum and  local maximum

Q: Find the values of a, b, c and d so that the curve f(x)= ax³ + bx² + cx + d has a local maximum at…

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Q: (х — 2)(х + 2)(г+ 1) (г + 3)(ӕ + 1)

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Q: create a graph with labels of a function that  satisfies:  have one point where f(x)=-3, at least…

A: Question- create a graph with labels of a function that satisfies:    have one point where f(x)=-3,…

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: Use a graphing utility to approximate (rounded to two decimalplaces) the local maximum value and…

A: Given: fx=x3-2x2-4x+5; -3<x<3 For finding values of local maxima and local minima, we draw…

Q: Draw the graph of f (x) = 3x +7/5x - 25 in the window [0, 25] by [0, 50]. Use the trace feature of…

A: Given: fx=3x+75x-25 in the window [0, 25] by [0, 50].

Q: Use limits to determine the equations for all horizontal asymptotes. 1- x y = x² + 1

A: To determine: The horizontal asymptote of the given function with the help of limits. Given…

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: A piece of cardboard measuring 14 inches by 10 inches is formed into an open-top box by cutting…

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Q: determine the local extremum point

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Q: True or false: Polynomial functions of degree 2 or higher have graphs that contain only rounded…

A: Consider the given information as Polynomial functions of degree 2 or higher have graphs that…

Q: 12. Explain in your own words the relationship between infinite limits and vertical asymptotes.…

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Q: Find it (giving both x- and y-coordinates) and determine if it is a relative maximum or a relative…

A: A critical point of a function is the point where the first derivative is equal to 0 or not defined.…

Q: First image is: Is that function diverges or converges? Second image is: Is that function diverges…

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Q: What are the Horizontal Asymptotes?

A: A horizontal straight line to which the graph of a function approaches as x tends to +infinity or…

Q: Determine the one-sided limit. Then indicate the equation of the vertical asymptote.

A: limx→π2 secxIf limx→a-fx≠limx→a+fx then the limit does not existlimx→π2secx=diverges

Q: Sketch the graph of a function with a jump discontinuity at x = 1. Then, evaluate the limits from…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

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Q: Explain the relationship belween horizontal asymptotes and limits

A: Explain the relationship between horizontal asymptotes and limit

Q: we need to endlose o field ith a rectangular fence. we have 500 feer of fencing material and a…

A: Given:           To enclose a field with a rectangular fence. We have 500 feet of fencing material…

Q: A). Domain, Symmetry, Asymptotes, Intercepts, B). f', Critical Points and Local Max/Min Values, C).…

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Q: Find the intervals where the curve is increasing and where it is decreasing. Also, find all z values…

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Q: Does not have any horizontal asymptotes

A: Function which does not have any Horizontal asymptotes

Q: 20. Use the ALGORITHM for curve sketching to sketch the graph of the function y = x³ – 7x +6 Do the…

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Q: 5. y=2sinx (0,27)

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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: Sketch the graph for this function

A: In this question. we draw the graph by using the calculus method i.e. by finding intercepts,…

Q: What are the three different types of asymptotes, and when do they occur?

A: The three types of the asyptotes are: 1. Vertical asymptote 2. Horizontal asymptote 3. Oblique…

Q: Find the limit 7x+2 limc I→∞ Va²+3 Does the function have a horizontal asymptote? If yes, what is…

A: Let's find.

Q: 3x2 If (x) = x² + 1

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Q: horizontial

A: To find horizontal asymptotes:   If the degree (the largest exponent) of the denominator is bigger…

Q: .An x by x square is cut from each corne of a rectangular sheet of cardboard tha is 8 inches wide…

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Q: B A,

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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…