15. Given, X-1 f(x) = x2-x a. Find the vertical asymptotes of the function b. Find the domain of the function. Answer in interval notation.

Q: 30. Consider the function defined by 0ifx 1 Sketch this graph and find all points where the graph is…

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Q: The graphs above are approximate graphs of f and f' for f(x) = x°(x – 12). So f is decreasing (and…

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Q: 7/8 For what value of x does the graph of f(x) = x8e* have a horizontal tangent?

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Q: Match the function with one of the graphs below using horizontal asymptotes as an ald. 4x f(x) = y 2…

A: Let's find horizontal asymptote of given function.

Q: Find the domain of function defined as follows. y = ln(x2 - 16)

A: y=lnx2-16Domain:       The domain of a function is the set of all possibleinputs for the function

Q: find the points of inflection and discuss theconcavity of the graph of the function. y=x-\ln x

A: Consider: y=x-ln x. Find the inflection points and concavity of function. First find the domain of…

Q: b) For f(x) = x²/(4 – x²), find the intervals in which it is increasing/decreasing, Concave down/up,…

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Q: 1. Given the graph of f', the derivative of f, locate all extrema of f. JUSTIFY. Minimum at x =…

A: To find the minima and maxima from the graph of f'(x)

Q: True or False The function f(x) = 2x/(x - 3) has y = 2 as a horizontal asymptote.

A: Given: fx=2xx-3 Concept Used: If degree of denominator is equal to the degree of numerator then…

Q: For what value of k will the function f be continuous on (-∞, 0)? { x2 – 16 if x + -4 f(x) = x + 4 k…

A: We have to find

Q: Suppose the function y = f(x) is increasing on the interval (−1, 5).• Over what interval is the…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: When a function is discontinuous at x=2, does that necessarily mean that 2 is not in the domain of…

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Q: 2. Given that f(x) = Vx+1 and g(x) =x² -9, find |(x) and give its domain in interval notation.

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Q: Show analytically (that is, without reference to a graph) that h(x) = v1 + x is always increasing,…

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Q: Describe how you could use the graph of f(x) = 2" to obtain a decimal approximation for V2.

A: y=2x

Q: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = f(x), evaluate…

A: Finding the g'(4) from the given conditions.

Q: Find the vertical and horizontal asymptotes of f(x) = cos x +4Vx

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Q: 12.x + 5x2 + 1 11. Determine the horizontal asymptotes of f(x): V16.x6 +6 1 12. Use the definition…

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Q: Explain why the graph of tanh x has the horizontal asymptotes y = 1 and y = -1.

A: Consider the given function fx=tanhx

Q: f(z) = z2

A: We have to show the given function is not analytic at any point.

Q: Let f(x)=-4cosx and g(x)=2cosx+3 for 0<x<2pi solve for f(x)>(g(x) on [0,2pi]. Write the…

A: Sketch the graph of -4cosx>2cosx+3 .

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

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Q: -7 if x 2. Sketch the graph of the function and use the limit definition of the derivative to show…

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Q: In the fucntion:  f(x)= (12-3x)(e^x)  When is the function concave up and concave down in interval…

A: Given,f(x)= (12-3x)(e^x) By definition,

Q: 3. For what value of x does the graph of f (x) = e* – 2x have a horizontal tange

A: Solve the following

Q: 2. For what values of x does the graph of f(x) = x³ + 3x² + x + 3 have a horizontal tangent line.

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Q: 1 Find the distance between the two values of x at which the function is discontinuous. x²-3x + 2

A: The function given is ,f(x) = 1x2-3x+2f(x) is discontinous when,x2-3x+2 = 0Using quadratic formula,x…

Q: Show that the line y x-1 is an oblique asymptote for the graph of y f(x), summarize all pertinent…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: 4. Find the intervals in which the function f(x) =x³ – 6x2 +9x +30 is concave up/concave down. Also…

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Q: given that the graph of f(x) passes through the point (10,9) and the slope of its tangent line…

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Q: The graph of  f(x)  and a line tangent to the curve at  x = 4  are shown. If  g(x) = sqrt(f(x))…

A: In the question it is asked to calculate the value of g'(4) for g(x)=f(x). for the graph given…

Q: given the function f(x)=axln(x+b), where function is decreasing at x=1-b?

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Q: Find a formula for a function that has vertical asymptotes x = 3 and x = 9 and horizontal asymptote…

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Q: Which of the following functions has a horizontal asymptote at y =-?

A: Here, the objective is to find the horizontal asymptote of the function.

Q: If f (x)= x2 - 4x, at which point on the graph f (x) is the tangent line horizontal

A: topic - slope of tangent line

Q: Show that the line y=x+ 1 is an oblique asymptote for the graph of y = f(x), summarize all pertinent…

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Q: Graph the function y =x + 1                                      x2+1 by applying the first and…

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Q: Find a formula for a function that has vertical asymptotes x = 6 and x = 8 and horizontal asymptote…

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Q: Let f(x) = e2sinx 1. Find the absolute extremum values off on the interval [7]

A: To find the extreme values of given function at given  interval.

Q: Q4:- Sketch the following functions showing the detailed steps in different graphs: h) f(x) = |Inx|

A: Sketch the following function showing in the given expression.  f(x) = 1/|lnx|

Q: Find the horizontal and vertical asymptotic for f(x)= 1/(1-x^2)

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Q: On the graph of f(x) = sec x and the interval [0, 2Δ), for what value of x does f(x)= -1?

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Q: Find a formula for a function that has vertical asymptotes x =1 and  x = 3and horizontal asymptote y…

A: Given that a function has vertical asymptotes x=1 and x=3 and horizontal asymptote is y=1. To find…

Q: 6. Determine the inflection points and intervals of concavity for the function y= e2*

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Q: 5. Find the length of the curve given by the graph of the function f(x) = x/x, for a in [1,4].…

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Q: The line tangent to the graph of f at x=3 is y=4x-2 and the line tangent to the graph of g at x=3 is…

A: Given that: The line tangent to the graph of f at x=3 is y=4x-2 and the line tangent to the graph of…

Q: 7. Determine the equation of the oblique asymptote for the following function. 4x? +7 x – 11 f(x) =…

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