Find the equation of the horizontal asymptote for the function f(x)= 2 - (x / x2 -25)

Q: Find the slope and the equation of the tangent line to the graph of the function at the given point.…

A: Given,f(x)= -2x +5 and the point (1-,7)

Q: find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the…

A: Consider the given function as fx=x-33x+4. The limit definition of the derivative of a function fx…

Q: Find the x-coordinates of all local maxima using the second derivative test. g(x) = a - 3x + 2

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Q: the derivative of the function by the limit process. f(x) = x²+x-3

A: Topic:- limits and calculus

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: By the fundamental theorem of calculus if we have F(x)=∫f(x)dx then F'(x)=f(x). In some cases an…

Q: -Find the range of the function y = 2 - sin3x

A: Introduction :

Q: Graph y = - x“ + 2x² – 10 function using x- and y-intercepts, critical points, points of inflection,…

A: Plot the graph for f(x).

Q: Ex.2 : Use first derivative , second derivative, and the graph y= x²-4 to asymptotes X-1

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Q: Find the slope and an equation of the tangent line to the graph of the function at the specified…

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Q: Find the relative extrema of the functions f(x)=-4x2-32x-62. Identify any maximum or minimum by…

A: Given function is Differentiating f (x) with respect to x, we get Now, we will find critical…

Q: A3) Find the equation of the line tangent to the graph of f(x) = 5x+7x ---.

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Q: Find f'(x). 6. f(x) = 4x + 7x f'(x) = Compare the graphs of f and f' and use them to explain why…

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Q: Find the points where the graph of the function has horizontal tangents. f(x) = 3x^2 + 7x - 5

A: We have to find the points where the graph of the function has horizontal tangents.…

Q: Use symmetry, first derivative, second derivative, and asymptotes to graph function:y: 2-x

A: The given function is y=x2-12-x ...............(1)

Q: Find the equation of the tangent line to the graph of the function f (x) = (x2 +8) (x - 3) at the…

A: Given : f(x) = (x² + 8)(x - 3) at the point      (1, -18)

Q: For the function f (x) = 2x° – 3x2 – 12x, use the First Derivative Test to find the location of any…

A: The given function is- fx=2x3-3x2-12x To find the critical points of a function- dfdx=0…

Q: Use derivatives to sketch the graph of f(x) = (x² – 8x + 16)e².

A: Given

Q: 3) Find the interval where the graph of f(x)= -2x' +3x +36x-1 is concave upward or concave downward.…

A: The given function is fx=-2x3+3x2+36x-1. Using second derivative test, the concavity as well as the…

Q: Use the limit definition to find the derivative of the function. f(x) = x2 – 4x +3 -

A: f(x)=x2-4x+3 TO find: The derivative using limit definition

Q: Find the x-coordinates of all local maxima using the second derivative test. g(x) = 2° – 3x7 +2

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Q: find the derivative using the definition g(x) = 2x2 + 1

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Q: Find the derivative of the funchion f(x)=9x-5

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Q: Find the slope m of the line tangent to the graph of the function f(x) = 5 - 6x at point (-1, 11)

A: Given:  f(x)=5-6x                y=5-6xDidderentating y=5-6x   with respect to 'x'  and substituting…

Q: OF(x)= - 2x3+ 84x2-72x on 7- -6x²+48 x-72=0

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Q: 3. Find all -values where the graph of f(x) = x³ + 3x² + x + 3 has a horizontal tangent line.

A: Solution is given below:

Q: For the function f(x) = 2x4 - 16x2 , find and identify any extrema (maximum/minimum) using the…

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Q: The graph of f(x)=2x^3+6x^2−144x+6 has two horizontal tangents. what are the positive and negative…

A: See the details solution in below

Q: Find the x-coordinates of all points where the graph of f(x) = 2x^3+9x^2-168x+21 has a horizontal…

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Q: 1. Find the derivative of f(x) = 3x³ + 2x using the limit definition.

A: We have to find derivative using definition.

Q: ve of the function using the definition of derivative. = V7- x 1 2 7-x n of the function. (Enter…

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Q: Find the equation of the secant line on the graph of the function f(x)=7x2 between the points where…

A: take x=-1 . take x=5

Q: The tangent line to the graph of a function f at the point x =2 has x-intercept 10/3 and y-intercept…

A: Given query is to find f(2) and f'(2)

Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

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Q: Find the derivative of f(x)= 5x² +2 using the limit definition of the derivative.

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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: 3. Use the limit definition of the derivative to find the derivative of the function. a) f(x) = 2x²…

A: Given query is to find the derivative using definitely.

Q: Find points of inflection of the function and determine the open intervals on which the graph is…

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

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Q: Sketch the graph of y= x²+ - by using the properties of the derivative. 2

A: To sketch the graph

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

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Q: Does the graph of y = sqrt(x) - ln x, x> 0, have an inflection point? Try to answer the question…

A: To determine if the function has an inflection point.Part (a) By GraphingPart (b) By Calculus

Q: sketch the curve f(x)= ln((x^2-4)/(x^2-3x-4))

A: given curve is                                                     f(x)=lnx2-4x2-3x-4 we have to…

Q: Find the slope of the line tangent to the graph of f(x) = 3x² - x- 5 at x = 1.

A: The equation of the curve is given by fx = 3x2-x-5 The point is x = 1 Formula Used: mtan = dfdxx=1…

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

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Q: How do you find the derivative of f(x)=5/1-8x using the definition of a derivative?

A: The given function is f(x)=51-8x

Q: find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the…

A: Given            fx=x-33x+4

Q: Use the First Derivative Test to find the x-value(s) at which the function 4 f(x) = x4 - 4x² + 1 X.…

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Q: Apply your understanding of derivatives to determine any intervals of increase for the function…

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

A: Application of Calculus.