OC userin Mathematics·11 Dec 201712. Exactly how many of the following four mathematical statements are always true: (i) The definite integral represents area under a curve or beneath a curve. (ii) The definite integral is a function obtained by taking the limit of a special sum. (iii) The definite integral of a function g(x) is a function G() such that G(x) dx = g(x) e is defined to be F(b) - F(a) where F is any antiderivative of (a) 4 (b) 3 (c) 2 (d) 1 (e) o
OC userin Mathematics·10 Dec 2017[10] 5. Consider P(R), the vector space of real polynomials of degree at most 2. with inner product <2,9 >= / p(x)(2) dr. Apply the Gram-Schmidt process to transform the standard basis {1,2,1?} for P(R) into an orthogonal basis.
OC userin Mathematics·7 Dec 20172. Let A be an n x n matrix. Which of the following statements are TRUE? (i) If Ax = b has a solution for every beR", then Ax = 0 has non-trivial solutions. (ii) If A is invertible, then Ax = b has a solution for every beR" (iii) If A is invertible, then AP is also invertible. (A) (ii) only (B) (i) and (ii) only (C) (ii) and (iii) only (D) (i) and (iii) only (E) (i), (ii), and (iii)
OC userin Mathematics·8 Dec 201713. Consider the following 3 curves: I. y=sin x + cos2x – sin 3x + 7.0 - 5. 11. y = 325 - 33 + 8x – 5. III y = ex48 + 3x25 + 35x + 15. Which of the 3 curves has (have) at least one horizontal tangent line? @ I and III only. ® II and III only. © II only. III only © I and II only.