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- What are the maximum and minimum values of the function y = | x | on the interval -1 ≤ x < 1? Notice that the interval is not closed. Is this consistent with the Extreme Value Theorem for continuous functions? Why?The fourth interaction when the positive x-intercept of the y=f(x) is approximated by the interval Halving method with initial approximations x1=1 and x2=4, has maximum error smaller than 0.1875 analyse using the graph below to determine weather the above statement is true or falseQ1 Integrate the following function using the trapezoidal rule with n=4 fz +12d 1(x x).x
- On the graph of f(x)=cosx and the interval [−2π,0), for what value of x does f(x) achieve a minimum? Choose all answers that apply.Find the maximum error if the approximation 1 + x + x2/2 is used to approximate ex on the interval [0,2] - using Taylor's inequality.On the graph of f(x)=sinx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?
- 10) The interval where f(x) = )=(√x+2) / x2 - 2x - 8 is continuous is ?Estimate the value of df/dx for f(x) = root 8x at x = 3, using any methodWe want to study the following function on the interval I = [−2; + ∞[ g(x) = 3x2+4x+3/x2+1 a) Calculate its derivative and its critical points. b) Calculate the following limit: c) Determine the table of variations of g in I. Deduce whether there are relative minima or maxima, an absolute minimum and maximum in I.
- For the function f(x) = cos2 x on [0,pi] a) find the critical points on the given interval b) determine the absolute extreme values of f(x) on the given interval when they existX^2+2*x on the interval 0 to 3 with a step size of .5 using trapezoid ruleUse the linear approximation (1 + x)k = 1 + kx to find anapproximation for the function ƒ(x) for values of x near zero. ƒ(x) = (1 - x)6