What are the asymptotes for tangent, contingent, secant and cosecant?

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 asymptote.  y = (sqrt(x2+9)/(sqrt(9 x2+1))

A: The given function is

Q: If you are given the equation of a tangent function, how do you find a pair of consecutive…

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Q: Find an eqaution of the line tangent to the graph f(x) = 3x2 - 5x at the point (1,-2).

A: fx=3x2-5x Slope of the tangent line is the derivative of the given function at the given point. So…

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

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Q: Use the Difference Quotient to evaluate the slope of the tangent line to the first parabola found in…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use the definitions of the hyperbolic functions to find each of thefollowing limits. limx→∞tanh x

A: We use the hyperbolic definition of tanh(x)

Q: Please show step-by-step solution!

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Q: Find the slope of the tangent line to the circle 4x² + 9y² = 36 at the point (0,2).

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Q: Define Vertical Asymptotes?

A: Vertical asymptotes

Q: By using differentiation, determine the width w that gives the maximum area A of the poster and show…

A: We have to find value of h & w for maximum Area.

Q: Define the term Asymptotes of Graphs?

A: Horizontal asymptote: The horizontal line to which a graph of the function approaches when x…

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: Define the term Horizontal Asymptotes?

A: An asymptote is a straight line that constantly approaches a given curve but does not meet at any…

Q: find the horizontal asymptote fon)

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Q: Define the horizontal Asymptotes?

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Q: Use the line tool to match the graphs with their discriminants.

A: Question 1,Given,         Gaphs of discriminant.

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: Find the points function' that have horizontal tangents when f(x) = x°-6x 6 On the graph of the

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Q: What is Oblique Asymptotes?

A: Oblique Asymptotes also known as the Slant Asymptotes. It is represented along a line y=mx+b, where…

Q: Describe the tangent line at an arbitrary point on the graph of y = 2x + 8

A: we have to describe the tangent line at an arbitrary point on the graph of y=2x+8

Q: What is the length of the curve y = sqrt(4-x2) from x = -2 to x = 1?

A: y=4-x2 Differentiating with respect to x, we get dydx=124-x2·d4-x2dx   ∵dxdx=12x=124-x2·0-2x=-x4-x2

Q: Determine the point(s) at which the graph of -8x f(x) = 2х- 1 has a horizontal tangent. (х, у) %3D

A: Solution - The derivative of a function is 0 at a point where the tangent is horizontal. Let us…

Q: How can we find the horizontal and vertical asymptotes of the curve?

A: We find the horizontal and vertical asymptotes of the curve

Q: There is no function with two different horizorntal asymptotes. True False 00

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Q: Find the slant asymptote with limits

A: Given function f(x)=(x-2)(x+2)(x+1)(x+3)(x+1)

Q: Show that the range of the tangent function is the set of all real numbers

A: The function tan returns a value of zero when the argument is zero. When increases to a value of 1…

Q: Find the tangent to y = sqrt(x2 - x + 7) at x = 2.

A: Given: -

Q: And show the asymptotes too.

A: Answer

Q: Use the definitions of the hyperbolic functions to find each of thefollowing limits. limx→-∞sinh x

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Q: Graph the function y = tan()+1 to the right on the interval (–2,2). In the space below, list all…

A: Given: y=tanπ2x+1; x∈-2,2

Q: nd all vertical and Horizontal asymptotes off Justify using limit stertennts. 6+3+4 ソー

A: We have to find aymptote

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: Define the Oblique Asymptotes?

A: To define oblique asymptotes.

Q: Define asymptotes?

A: To define: Asymptotes of the curve. Explanation: The asymptotes of the curve is a tangent to the…

Q: Does not have any horizontal asymptotes

A: Function which does not have any Horizontal asymptotes

Q: What are the asymptotes?

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

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Q: Find all points on the semicircle, y=sqrt 7-x^2, at which the slope of the tangent line is equal to…

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Q: Define the term asymptotes?

A: An asymptote to the curve can be considered as a line to which that curve converges.

Q: Con sider the funtion fex)=1 X+3 alt A) using a limit, Sh ow that Part B) Fid the eauation of the

A: Here, the given function is: f(x)=1x+3

Q: Q1. Using Lopital Rule ,Find :lim -cos

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: use the ,8 de linit of the funchions ho prove that : Lim J19-X =3

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Q: Differentiate the following hyperbolic functions.

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Q: What are the Vertical Asymptotes?

A: Vertical Asymptotes are the vertical lines that represents the zeros of the denominator of a…

Q: The slope of the line tangent to the graph of position as a function of time at t = to

A: The slope of the line tangent is in the form of a difference quotient approach t=t0 is, m=ft-ft0t-t0

Q: horizontial

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

Q: By total differentiation, determine or find the approx. change in the length of the hypotenuse of a…

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Q: when i am asked to graph a tangent, cotangent, csc, sec. how do i label my x-axis? i am supposed to…

A: To plot the graphs mentioned above, The scale will have to be real numbers.  Plots of tan,…

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.