What is Secant: Definition and 61 Discussions

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.

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  1. rocomath

    How do I find the equation of a secant line using two given points?

    Wow, someone asked me this question and I'm stumped. Find the equation of the secant line that contain P[0,f(0)] and Q[3,f(3)] Am I given enough information to solve this? m=\frac{f(x+h)-f(x)}{h} ... m_1=\frac{f(h)-f(0)}{h} m_2=\frac{f(3+h)-f(3)}{h} That doesn't really help me though...
  2. D

    Find the Slope of the Secant Line PQ for x-values .5 to 1.001

    The point P(1,51) lies on the curve y=46 x2+5. (a) If Q is the point (x,46 x2+5), use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the following values of x. .5, .9, .99, .999, 1.5, 1.1, 1.01, 1.001 I plugged all of the values of x into...
  3. Z

    Help with secant question , thanks

    here is my question, *thanks for helping* i need it badly Consider the curve y = f(x) where f(x) = (x-5)(2X+3) A) Show that P1 = (x1,y1) = (0,-15) is on the curve and find and expression for the slope of the secant joining P1 with any other point P2 = (x2,f(x2)) , x2 cannot be 0 on the...
  4. R

    Proving slope m of a secant connecting two points of the sine curve

    Proving slope "m" of a secant connecting two points of the sine curve Homework Statement Write and expression for the slope m of the secant connecting the points Po(Xo,Yo) and P(X,Y) of the sine curve. Use the appropriate trigonometric identity to show that m= sin((X-Xo)/2)/((X-Xo)/2) * cos...
  5. A

    Integtrating secant and tangent

    Homework Statement (integrate)sec^3(2x)*tan(2x)dx Homework Equations The Attempt at a Solution Okay, so first I tried to separate secant and tangent, to get (integrate)1/cos^3(2x) * sin(2x)/cos(2x)dx. The u would be cos(2x), the du would be -du=sin(2x)dx. I subsitute these...
  6. S

    Integral of Secant: Solving for \int \frac{1}{cosx} dx | Step-by-step Solution

    Homework Statement Basically, I have to find \int \frac{1}{cosx} dx by multiplying the integrand by \frac{cosx}{cosx} I go through and arrive at a solution, but when I differentiate it, I get -tan(x) something's clearly wrong, but I can't see what it is that I'm doing wrong...
  7. W

    Why is the Absolute Value of X Taken in the Derivative of Arc Secant?

    Hello there In the derivative of the arc secant, why is the absolute value of x ( which is present in the denominator) taken? Is this to prevent the possible of having a zero ( and making the whole expression undefined ? ) Thanks
  8. F

    What is the Antiderivative of Secant with a Non-Integer Power?

    For one of my homework assignments, I had to find the integral of a function. I got my function simplified to sec(t)^(8/3). I tried to use the reduction formula for sec(t)^n, but I believe that it only works if the power of sec is an integer. Could somebody help me out, please? Edit: I...
  9. T

    Tangent and Secant Function Applications

    Hello all, I have a question concerning the Tangent and Secant Functions (the graphs). I cannot think of a way that either of these can be used in the real world. I need to find applications for these. For example, the sine function can be used to represent waves or periodic motion... but...
  10. F

    How to find the integral of the secant function

    \int \sec hx I solve it in this way: \int \arccos hx \int \ln (x^2 + \sqrt{x^2 -1}) dx Then, I substitute u = \ln (x + \sqrt{x^2 + 1}) then I get x\ln(x + \sqrt{x^2 + 1}) - \int x/\sqrt{x^2 + 1}dx and then I substitute v = x^2 + 1 x\ln(x + \sqrt{x^2 + 1}) -1/2 \int v^(1/2) dv...
  11. S

    Calc Question: Finding Secant Slope?

    I wrote down the notes from class, but when I tried to do the homework, I am not even close to the right answers. The formula I wrote down is: \frac{-1}{(x)(x+h)} Apparently that's wrong. Anyone know what it's supposed to be?
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