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(2 homework)

E.K. Shidlovskaya Mathematics Homework 2 Variant 9 Part 1. 1. Find the following limits a) lim - n -5 b) lim n -5 c) lim * - 25 d) lim X' - 81 n->oo 6n +1 n->0 6n- + 1 x -+ 9 x -2 x - 9 2. Find asymptotes (vertical, horizontal, slant) of the following functions a) y =- 2x - 2 b ) y = 8x2 + 3 (x-9)2 4x - 5 c ) y = - 4x - 1 3. Find derivatives of the following functions a) y =x12 b) y = 2x +8x2 - 7 c) y = x sin x d) y = (x0 - 10) In x e) y = el2x f) y = cos(x2 +11) g) y = In(sin 12x) h) y = elox cosxll 4. Find the following differentials a) d(xl) b) d(x12 - 6) c) d(sin 10x) d) d(cos(x* -10)) e) d(elox ) f) d(x cosllx) g) d(In(x3)) h) d(ell sin(x10 )) 5. Find increase and decrease intervals, minima and maxima of the following functions a) y=x' + 12x + 45x +5 by=-x' -6x2+63x-9 c) y= (x -30)e2x