If æ = 1 is a vertical asymptote of y = f(x), then f is not defined at æ = 1. True False

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: Determine which among the following curves has a horizontal asymptote at y=O. * x +1 x² – 1 f (x) :…

A: →Check degree of numerator and denominator . →Degree is the highest power of polynomial. →When…

Q: Find the Arc lenght of the graph of the function f(x)=(4/5)x^5/4 on (0,4)

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Q: ) Find a function ƒ such that f'(x)= x³ +3 and such that the line y+5x O is tangent to the graph of…

A: Given, f'(x) = x3+3  and the line  y +5x =0 is tangent to the graph of f   Let's assume the function…

Q: Determine analytically the point (s) at which the graph of the function has a horizontal tangent. x2…

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Q: x²-1 If f(x) = for x +1 and f(x)=2 when x 1, show that the function x-1 is continous at x=1?

A: Show that f is continuous at x=1

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: 9. Show that for f(x) = x° we have f"(0) = 0 but the point x = 0 is not an inflection point of f.

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Q: Given the graph of the derivative f'(x) shown below, which one of the following statements regarding…

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Q: Suppose that the di’erentiable function y = g(x) has an inverseand that the graph of g passes…

A: Differentiable function y=g(x) ha an inverse ; Graph of g passes through the origin with slope 2;

Q: Which of the following functions has a horizontal asymptote at y = 2?

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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: 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: when x # 1 Show that f(x)% = 2 when x =1 is discontinuous at x 1

A: Given query is to find the continuity of the function at x = 1.

Q: The function g is difirentiable and satisfies g(-1)=4 and g'(-1)=2. what is the approximation of…

A: given g(-1)=4 and g'(-1)=2.         g(-1.2)=?

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: The line tangent to the graph of g(x) = x³ – 4x +1 at the point (2, 1) is given by the formula L(x)…

A: To select: The correct options. Given: The function is g(x)=x3-4x+1 and the line tangent to the…

Q: Find the domain of function defined as follows. y = ln(x + 7)

A: Given       y = ln(x + 7)

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: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: If the line x = 1 is a vertical asymptote of y − fsxd, then f is not defined at 1.

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Q: The function f(x)=(1/(x+1))+4 is decreasing on what interval(s)?

A: Consider the function  fx=1x+1+4

Q: find the tirst asymptote of y = Tan(sx) %3D

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Q: Determine the equation of the function f(x) if it has a hole (point of discontinuity) at (6,3) and a…

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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: Suppose g(-2)=3 and g'(-2)=-4. Let f(x) = x3 + g(x). Find the equation of the line tangent to y =…

A: Given,     f(x)=x3+g(x)

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: The horizontal asymptote for f(x) = sin(x) is %3D 2x

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Q: * TO 7. Determine a function whose graph has vertical asymptotes at x = ±2 and a horizontal…

A: The objective is to determine the required function.

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

A: To find: The value of g'(4) if g(x)=f(x). Concept used: Chain rule: f(g(x)=f'(x)g'(x)

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: What is the equation of the vertical asymptote of f(x) = tan x where 0 < x < n

A: First draw the graph and get the vertical asymptot.

Q: The distance between the x-intercept of the tangent line to the curve y = and the x-coordinate of…

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Q: If the line y = 2 is the horizontal asymptote of the curve y = f(x), then /(2) is undefined. Select…

A: To find whether given statement is true or false.

Q: The graph of f (x) = ax+b x²+3x-8 has horizontal tangent at (2, -1). Determine the values of a and…

A: Given query is to find the value of a and b.

Q: 2. Find the horizontal asymptotes of the graph f(z) = %3D 3. Differentiate f(x) = – using the limit…

A: 2. To find the horzontal asymptotes of the graph f(x)=x2-2|x|3+13.  To find the derivative of…

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: suppose the line tangent to a graph of f at x = 4 is y = 3x+2 and suppose y = 5x -3 is the line…

A: Given information:The line tangent to a graph of f at x = 4 is y = 3x+2 and suppose y = 5x -3 is the…

Q: *** Use the first and second derivative to sketch the graph of f(x) = In(x² +1). In particular,…

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