In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method. However, the secant method predates Newton's method by over 3000 years.
Slope of a Tangent Line For f (x) = x^2 − 1:
Find the slope of the secant line containing the points P = (−1, f (−1)) and
Q = (−1 + h, f (−1 + h)).
Solution:
I think I need to find f(-1).
f(-1) = (-1)^2 - 1
f(-1) = 1 - 1
f(-1) = 0
Point P becomes (-1, 0).
I now must find f(-1 + h)...
Slope of a Tangent Line For f (x) = x^3.
(a) Find the slope of the secant line containing the points (2, 8) and (3, 27).
(b) Find the slope of the secant line containing the points (2, 8) and (x, f (x)), where x does not equal 2.
For (a), I just have to find m, the slope using m = delta...
Attempt : I could not progress far, but the following is what I could do.
$$\begin{align*}
\mathbf{\text{LHS}} & = (\tan A+\tan B+\tan C)(\cot A+\cot B+\cot C) \\
& = 3+\tan A \cot B+\tan B \cot A+\tan A \cot C+\tan C \cot A+\tan B \cot C+\tan C \cot B\\
& = 3+\frac{\tan^2A+\tan^2B}{\tan A \tan...
The Secant Method is a numerical scheme to solve equations of the form $\displaystyle f\left( x \right) = 0 $, so we must rewrite the equation as $\displaystyle 0 = \frac{1}{2}\,x^2 - 10 - \sin{ \left( 1.8\,x \right) } $.
Thus $\displaystyle f\left( x \right) = \frac{1}{2}\,x^2 - 10 - \sin{...
$\tiny{3.2.15}$
Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. Graph the function the secant line through the endpoints, and the tangent line at $(c,f(c))$.
$f(x)=\sqrt{x} \quad [0,4]$
Are the secant line and the tangent line parallel...
Task
Use the Bisection, Newton, and Secant methods to solve (to at least 8
signicant figures) the equation
sin(x) = 0.98 cos(2x2)
over the interval [0, 2.5], in radiant units. For the Newton method, try with
several different initial guesses including x0 = 1. With the Secant method,
use the same...
Homework Statement
Find dy/dx for ##~y=\sec^2(5x)##
Homework Equations
Secant and it's derivative:
$$\sec\,x=\frac{1}{\cos\,x}$$
$$\sec'\,x=\tan\,x\cdot\sec\,x$$The Attempt at a Solution
$$y=\sec^2(5x)~\rightarrow~y'=2\cdot 5 \cdot \sec(5x)\tan(5x)\sec(5x)=10\tan(5x)\sec^2(5x)$$
The answer...
Homework Statement
Solve ##\displaystyle{d\sigma = \frac{d\rho}{\cosh\rho}.}##
Homework Equations
The Attempt at a Solution
The answer is ##\displaystyle{\sigma = 2 \tan^{-1}\text{sinh}(\rho/2)}##. See equation (10.2) in page 102 of the lecture notes in...
Homework Statement
This picture:
http://i.imgur.com/n015WjU.png
It's drawn with exactly the amount of information from the worksheet. Specifically, the two secants meet at a point, with an angle of 28 degrees between them. Both secants partition off an arc of 120 degrees. The goal is to...
stevendaryl submitted a new PF Insights post
Solve Integrals Involving Tangent and Secant with This One Weird Trick
Continue reading the Original PF Insights Post.
Homework Statement
The two graphs are possible legitimate representations of ##y=\sec^{-1}(x)##.
The derivative is positive on all the domain and so is graph A, but graph B has negative tangent when x<-1
Homework Equations
Derivative of inverse secant...
Homework Statement
I am having some trouble understanding the following solved problem:
Use two iterations of the Secant method to estimate where ##x^2 -x## has a local minimum. Start with ##x^{(0)} =1##, ##x^{(1)} =1/2.##
Answer:
Homework Equations
Secant iteration:
$$x_k = x_{k-1} -...
Homework Statement
The points P (2,-1) and Q (3,-4) lie on the parabola y = -x2+2x-1
a) Find the slope of the secant line PQ.
b) Find the slope of the tangent line to the parabola to the parabola at P.
c) Find the equation of the tangent line at P.
Homework EquationsThe Attempt at a Solution
I...
Homework Statement
I need to find the roots of a given equation using the secant method and matlab. I have already found all the roots, but I am also asked to find the rate of convergence for the method empirically, meaning that they want me to find the order of convergence through the set...
Since learning about being able to complexify differential equations (I am doing the MIT OCW course by Arthur Mattuck), I have tried to apply to this to particular problems in integration as well. Specifically, I have tried to integrate the secant of some function to see if it would lead to the...
Hey, everyone.
I am trying to find the power series of secant from the known power series of cosin, but my answer does not match up with Wolfram and Wikipedia.
I know:
cos(\theta) = 1 - \frac{1}{2}x^2 + \frac{1}{4!}x^4 + ...
So, using the first two terms (assuming a small angle)...
The question was too long to post in the title so I just wrote down the first part. I hope this is alright. Here is the question that I am doing right now:
This is the graphical representation (thanks to Desmos Graphing Calculator):
So I have substituted the points in the equation to get...
Homework Statement
sec(5x)-5=0
Homework Equations
The Attempt at a SolutionI turned it into 1/cos(5x)=5 x=θ/5
then i switched it to cos(5x)=/1/5
Then cos-1(1/5)=θ which = 1.36 (one solution) then divided by 5 which is .2738 which works as one solution
since the positive cos is in the 1st...
Homework Statement
1. For the curve y = x^2+ x, and the point P (1,2)
a) determine the slope of the secant mPQ if Q(2, 6)
b) what is the slope of the secant if Q is at the following values of x
1.5 1.1 1.01 1.001
c) Estimate the value of the tangent to the curve at P. Reason...
So I know that sec(x) has period 2Pi, and it's even so I don't need to figure out coefficients for bn.
Let's take the limits of the integral to go from -3/2 Pi to 1/2 Pi. How do I integrate sec(x) sin(nx) dx?! Am I on the right path?
PS: I know that this doesn't satisfy the Dirichlet...
Homework Statement
Hi there!
I'm just trying to figure out the Fourier transform of the hyperbolic secant function... I already know the outcome:
4\sum\ ((-1)^n*(1+2n))/(ω^2*(2n+1)^2)
But sadly, I cannot figure out how to work round to it! :( maybe one of you could help me...
Homework...
Homework Statement
Find the slope of the line that joins P (0,2) and Q (x, 2^x+1) for x ≠0. type the expression using x as a variable. Homework Equations
Rise over Run?
The Attempt at a Solution
I have a picture of the graph but i don't really know what to do, Please help.
I graphed it at x=...
Homework Statement
If the power of the secand is even and positive..
\int sec^{2k} x tan^{n} x dx = \int (sec^2 x)^{k-1} tan ^n x sec^2 x dx The Attempt at a Solution
The way I see it,
sec^{2k} x = sec^2 x dx * sec^k x dx
the next step seems to be to break down sec^k, but on closer...
Homework Statement
Find the derivative of sec^{-1}(\frac{\sqrt{1+x^{2}}}{x})
Homework Equations
sec^{-1}=\frac{U'}{U\sqrt{U^{2}-1}}
The Attempt at a Solution
U'=-\frac{1}{x^{2}\sqrt{1+x^{2}}}
U\sqrt{U^{2}-1}= \frac{\sqrt{1+x^{2}}}{x^{2}}
Therefore the derivative is...
I'm trying to understand something in Fermat's Theorem. I can't really phrase it in words, but I will write what my textbook says.
Apparently if
\lim_{x→c}\frac{f(x)-f(c)}{x-c} > 0
then there exists an open interval (a,b) containing c such that
\frac{f(x)-f(c)}{x-c} > 0 for all...
Homework Statement
what is sec(pi/4)
what is sec(0)
The Attempt at a Solution
First let me make sure that cos^-1, acos and sec, they are all the same right?
I put in cos^-1(pi/4) in my calculator and the answer I get is .667, which I think is the same as sec (pi/4). The book...
Homework Statement
Homework Equations
The Attempt at a Solution
I don't see how they get from step one to two. I would think both secants would cancel since one is positive and the other is negative but that doesn't happen. i think i understand the manipulations of the tangents but not...
Homework Statement
Compute the following partial sum
\sum_{k=0}^n\frac{1}{2^{2^k}+2^{-2^k}}
Homework Equations
The Attempt at a Solution
So far, I've tried transforming the terms into secant hyperbolic functions...
Homework Statement
Homework Equations
How did they come up with \frac{1}{2}+k for the equation of the vertical asymptote? I understand everything else except this.The Attempt at a Solution
On this particular exercise, I graphed it and saw that each of my vertical dashed lines were all one whole...
The Problem is when I Compute the Inverse I have to solutions
sech^{-1}(x) = ln(\frac{1\pm \sqrt{1-x^{2}}}{x}) : 0<x\leq 1
And this not function which of them I will choose
Another Question is how can I prove without the graph that csch (x) is one - to -one
thanks
Hi so I have attached a graph, and I am trying to find the first root of the function. I began using Newton Raphson however due to the oscillatory nature of the curve, sometimes NR would not find the first route but an nth route. I need the first. Therefore what I did was compute the first time...
Homework Statement
Why is Cosin and Secant even? Cos (-t) = cos t, Sec (-t) = sec t
Why don't they equal - sec t instead like the rest of the functions? Thanks
Homework Equations
The Attempt at a Solution
Homework Statement
Find the value of y = sec^-1(9s^4 + 7) with respect to s
Homework Equations
The Attempt at a Solution
secy = 9s^4 + 7
but where do I go from here?
Homework Statement
Given a point P (3, 10) and the equation of a curve as x^2 -5x-4, find the slope of the secant and the equation of the tangent line to the curve
Homework Equations
The Attempt at a Solution
I tried using y = f(x + h) -f(x) all divided by h and got (x + h)^2 -...
I try to solve this equation with secant method in MATLAB.
fn=40*n^1.5-875*n+35000
my initial guess is n1=60; n2=68; I want to find root and absolute relative approximate
error at the end of each iteration. I have an infinite loop. Can you help me repair my file?
This is my m-file...
Homework Statement
There are two parts to this problem.
On the curve 2x^2-5 lie two points P and Q. Let the abscissa of P be "x" and the abscissa of Q be "x+h". No numerical coordinates are given.
a) State the coordinates of P and Q.
b) Using these points find the gradient of...
So I have studied some of the Numberical methods such as Newton Raphson etc, but I want to try and solve this particular problem using the secant method. The problem is something I am reading in an article, and I am trying to follow the maths through.
I am slightly wondering though how it is...
I am math teacher and was asked the classic question, "Where am I ever going to use this in life" I usually have a real word example, but for the cosecant function I am stuck (Besides higher level math classes.) Anyone know a specific example?
This is a continuation of my previous post, so please bear with me
Homework Statement
Find the zeroes of the following function:
y= 2 sec (-2x+180deg) + 3Homework Equations
Break down the equation into:
y= 2 sec -2(x-90deg) + 3;
Finding zeroes, means finding the x values when y=0...
TI-83 problem...Secant Graphs
Homework Statement
What are the properties of:
y= 2 sec(-2x + 90deg) + 3
Homework Equations
sec (x) = (1/cos (x))
The Attempt at a Solution
I have a problem with finding the Domain of y= 2 sec(-2x + 180deg) + 3.
First of all, I have to put the...
Hi,
Did anyone know how to do the Fourier transform of the hyperbolic
secant? I know the answer; it's given in the text (I'm reading
Ablowitz, Fokas, Complex Variables), it's another hyperbolic secant,
but I want to know how to do it. My dilemma is:
a) what contour to use? I'm having...
Homework Statement
Reduce to a single term:
I really have been spending a wretched time to solve that
tan (x/2)*(1+sec x)(1+sec 2x)(1+sec 4x).......(1+sec (2^n)x)
Homework Equations
tan (x/2)=2 tan (x/4) / 1- tan^2 (x/4)
can this ever help 1+tan^2=sec^2
The Attempt at a...
I am working on a MATLAB program to find the optimum heating of a heater. I am having a hard time applying the secant rule and really have no idea how to apply this rule in general. If someone could shine some light on the subject that would be great.
so i worte this and it works somtimes. the function I am trying to find the roots of is
2x^3 - 6x^2 + 3x + 1
the program i wrote will find two of the roots but i can't get the third. I know the secant method it sensitive to the interval that you pick so i was thinking that was the...
I have not seen math in years and just started claculus last week.
Homework Statement
The point p(25,7) lies on the curve y=\sqrt{}x+2. Let Q be the point (x, \sqrt{}x+2).
Find the slope of the secant line PQ for the following values of x:
If x=25.1, the slope of PQ is:
Homework...