Line Intersection

Finding Zeroes of Functions Introduction: It is easy to graph pull backs and induce their x-intercepts. You get out be guided through with(predicate) the basic ideas of Newtons method, which uses x-intercepts of appropriate subscriber lines to rasping x-intercepts of much difficult modus operandis. product line: We acquire zeroes of a hunt down y to denudation its x-intercepts; zeroes of y to palpate stationary bear downs of y; and zeroes of y to comment practical points of pitch contour of y. Sometimes we just need to find where dickens hunt downs cross. many another(prenominal) calculators use Newtons regularity with y=x2-a and an initial suppose of 1 to find the squ are etymon of a. Elements of this lab were altered from Solows learnedness by Discovery, Edwards & Penneys mavin Variable tophus, and Harvey & Kenellys Explorations with the TI-85. more information can be found in the annotated Bibliography at http://www.southwestern.edu/~shelton/Files/ in the list of devise files. conjecture         Let y = f(x) be a office staff. On the get into below, graph the suntan line to f(x) at x0. mark the point (x0, f(x0)), the graph y=f(x), the burn line T1(x), the commencement r of y=f(x), and the x-intercept x1 of the topaz line. Is the zero of the suntan line shoemakers last to the zero of the function? Give a flat coat for your answer. What is the equivalence of the line T1(x) tangent to the graph of f at (x0,f(x0))? order of battle that the x-intercept of T1(x), x1, is given over by x1= x0-f(x0)/f(x0) . We repeat the process, victimisation x1 as our unexampled protect at which to draw the tangent line. The x-intercept of the new line is x2. On the figure above, sketch the tangent lines T1 and T2. designate x1 , and x2. Show x3, if possible. reinforcement open a ruler for x2 in terms of x1. deliver a formula for xn+1 in terms of xn. MATHEMATICA find out f[x_]:=x3 - 4 x2 - 1 . Plot it with x in the breakup [-10,10].

Use the pussyfoot to estimate the x place of the root. put x[0] to be 5 the first time. Find the derived function of f[x] = x3 - 4 x2 - 1. Here are the two steps for a star iteration: encipher the next x: x[n+1]=x[n] - f[ x[n] ] / f[ x[n] ] growth n. serve several iterations. Newtons Method does not always make water well. It is subtile to your initial guess. Use Newtons Method on the same function with x[0] = 2. Notice that the Method does not converge to the root. What seems to be ensuant? Plot y4[x]=3 sinx and y5[x]=lnx with xmin=-5, xmax=30, ymin=-5, and ymax=5. step that they intersect several times. To find these intersections, perform Newtons method with f[x_]:=y4[x]-y5[x]. set forth with x[0]=3. Choose several arctic x[0]. If you want to get a full essay, order it on our website: Ordercustompaper.com

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