1. Sketch the function Ax) = 3x* - 12x', indicating any extrema, points of inflection, and vertical asymptotes.

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: 3. Determine the slope of the tangent at x = -1 on the graph f(x) = (5x² + 1)3.

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Q: Please show step-by-step solution!

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Q: Suppose that the tangent line to the graph of a function f at x=2 passes through the point (5,19)…

A: Given that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and…

Q: Find the points of discontinuity of the function f(x)=arctan1x if they exist.

A: The given function is not defined at x = 0. Now the left hand limit at x = 0 is, And the right hand…

Q: 4. Find the slope of the tangent to the graph of f (x) = x³ + 3x² + x at its point of inflection.…

A: Slope of the tangent is obtained by dy/dx

Q: Find the length of the curve of the graph of the indicated function. y = In(sen x), between points…

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Q: 3. If y = 2 – 1, find the length of the graph of f from point z = 0 to a = 1.

A: Here, the given function is: y=f(x)=423x-1 To find the length of the curve from x=0 to x=1

Q: Solve for the slope of the functions at the points specified using the limit definition of slope of…

A: Consider the function  f(x) = 12x2− 9x + 15 point (−2, 81).

Q: 2. Sketch the function f(x) -1 indicating any extrema, points of inflection, and vertical asymptotes…

A: Solve the following

Q: Sketch the curve if y' is negative and y'' is negative on the interval of (-infinity, -3) with a…

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Q: 14. Find a function whose tangent has slope 4x+1 for each value of x and whose graph passes through…

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Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent.

A: Given that  f(x)=(-8x)/(√(2x-1))  The function has a horizontal tangent  To find the point at which…

Q: Use the alternate definition, lim Ax)-Aa) to determine the instantaneous rate of X- a change of Ax)…

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Q: The tangent lines to the graph of f(x) =x² grow steeper as x in- creases. At what rate do the slopes…

A: Given function is, f(x)=x2

Q: Find the tangent line to the graph of f(x) = 3ex - 5x2 at x = 2.

A: A line is generally an object in geometry that doesn't bend i.e. it has no curve. It is a collection…

Q: 9) Write an equation of the tangent line to the graph of y = 5x2 - 8 at the point where x 0. %3D -3x…

A: Quotient rule of derivative of the function f(x)=u(x)/v(x) is

Q: The slope of the tangent line to the graph of the function y = 7Vx – 3 at (9, 18) is - O 3 - 2.00 O…

A: Simply take the derivative of the function at that point.

Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

Q: What conditions must be satisfied by a function if it is to be con-tinuous at an interior point of…

A: A function is continuous at an interior point c of its domain if

Q: Find the equation of tangent line to Graph of f(x)=3 x In(5x-4) at point where x=.1

A: Solution:

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: Give the formula for a function which has vertical asymptotes at x=7 and x = -6 but is otherwise…

A: A function has vertical asymptotes at x=7 and x=-6 but is otherwise continuous.

Q: 4. Sketch the function Ax) = 2xª – 16x², indicating any extrema, points of inflection,

A: follows the procedure given below.

Q: Show with the middle value theorem that the second derivative f'′ has at least one zero (for this…

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Q: Suppose that a one-to-one function f has tangent line y=5x+3 at the point . (1,8)Evaluate (f-1)'8

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Q: Find the limit as x approaches infinity of f(x) when f(x) is x times square root of x

A: x times sqrt(x)= x times x^(1/2)= x^[1+1/2] = x^(3/2)

Q: 5. Determine the slope of the tangent at point (1,5) on the graph of f(x) = (9 – x²)} + 1.

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Q: 6. Prove if the following function is differentiable y2 = (arctanx + 1)°*

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Q: 3 Show that f(x)= 1x-5 is NOT differentiable at 5 by using the defini tion of the derivative, (Start…

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Q: Compute the equation of the horizontal asymptote of the curve y = (2x- 1)/ (x + 2). y = 2 x = 2 X =…

A: Given; y=2x-1x+2   As we know that; To calculate the horizontal asymptote, solve the limit…

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: 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: The ________ of a sine or cosine curve represents half the distance between the maximum and…

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Q: Express the length l of a chord of a circle of radius 8 as a function of its distance x from the…

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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: 5. Consider two entire functions with no zeroes and having a ratio equal to unity at infinity. Use…

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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: show that the function has neither an absolute minimumnor an absolute maximum on its natural domain.…

A: y=2x-sin2x The domain of given function is -∞, ∞. The range of sin2x is -1, 1.

Q: Prove without graphing, that the graph of the function has at least two x-intercepts in the…

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Q: FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF THE FUNCTION f(x) = 5- x2 AT (3,–4). %3D

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Q: Determine the area of the triangle formed by the tangent to the graph of the function y=3-x2 drawn…

A: Given,            y = 3 - x2 , and the point 1, 2

Q: find the slope of the tangent line to the graph of the function at the given point. f(x) = -2x + 5…

A: Given:

Q: Find an approximation that is accurate to three decimal places to the zero of f (x) = x³ -3x- 1 in…

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Q: List all the vertical asymptote(s) for the function y=tanx for 0≤x≤2л

A: Application of Calculus.

Q: #8.) Determine the slope of the tangent at point (1,4) on the graph of f(x) = (9-x²) ²/

A: Topic = Derivative As per guidelines , At a time only one question can be answered. Please repost…