4. For computing the integral √7/2/2 cos(x) f(x) dx, find a two point quadrature formula S2(f) = c1f(x1) + C2f(x2), which is exact for all polynomials of a maximal possible degree.

For the following exercises, use the Intermediate Value Theorem to confirm that the given polynomial has at least one zero within the given interval. f(x)=x52x, between x=1 and x=2.

A path of a toy rocket thrown upward from the ground at a rate of 208 ft/sec is modeled by the quadratic function of. h(x)=16t2+208t. When will the rocket reach its maximum height? What will be the maximum height?

Consider the following rational functions: r(x)=x2x22x1 s(x)=x2+4x3+27 t(x)=x+2x39x u(x)=x225x2+x6 w(x)=x+3x3+6x+9x (a) Which of these rational functions has a horizontal asymptote? (b) Which of these functions has a slant asymptote? (c) Which Of these functions has no vertical asymptote? (d) Which Of these functions has a "hole"? (e) What are the asymptotes of the function r(x) ? (f) Graph y =u(x) , showing clearly any asymptote and x- and y intercepts the function may have. (g) Use long division to find a polynomial P that has the same end behavior as t. graph both P and t on the same screen to verify that they have the sane end behavior.