Are the following statements true or false? Choose True if the statement is always true, and otherwise choose False.

? 1. The Taylor polynomial provides an approximation for a function that is always an underestimate of the unction because we haven't yet added up all terms. 2. The linearization of f at x = a is just another name for the tangent line to f at x = a. ? 3. Quadratic approximations are always better than linear approximations on larger intervals around the center a = a. ? 4 4. If In (a) is the nth Taylor polynomial of a function f (x), centered at x - a, then all derivatives of Tn(x) and f (x) are equal at x = a.? 5. If f is a quadratic polynomial, then all Taylor polynomials Tn of f with n > 2 will be the same, namely the function of itself. ? 6. Factorials appear in the denominators of terms in Taylor polynomials due to the fact that the nth derivative " [x"] is equal to n! for all n - 0, 1, 2, . . .. 7. Let T3() be the degree 3 Taylor polynomial of f(a) centered at x = 0. Then f()(0) must be different from T.) (0).8. If two functions have the same degree 2 Taylor polynomial, then the two functions must be equal. ? 19. The Taylor polynomials for f (x) - sin(x) and g(x) - cos(x) are quite similar, except one set has only even degree terms and the other has only odd degree terms; a convenient way to remember which is which is to think about even and odd functions. ? 10. When plugging values for a into the Taylor polynomials of trig functions, we have to make sure that these values are in degrees, not radians, because it is simpler to work in degrees