Linear Equations Part 2 | Felician University

University:
Felician University
Course:
MATH-002 | Basic Math Skills-Algebra
Academic year:

2020
Views:

379

Pages:

6
Author:

StellarSymphony

ASSIGNMENT 1.3 PART 2 P.85-86 lim(x->0) sin(x) / 5x = lim(x->0) 1/5 * sin(x)/x = 1/5 * lim(x->0) sin(x)/x = 1/5 * (1) = 1/5 lim(x->0) (sin(x)(1-cos(x))) / x^2 = lim(x->0) (sin(x)/x * (1-cos(x))/x) = lim(x->0) sin(x)/x - lim(x->0) (1-cos(x))/x = (1)(0) = 0 lim(x->0) sin^2(x) / x = lim(x->0) (sin(x)/x * sin(x)) = lim(x->0) sin(x)/x * lim(x->0) sin(x) = (1)(0) = 0 lim(h->0) (1-cos(h))^2 / h = lim(h->0) ((1-cos(h))/h * (1-cos(h))) = lim(h->0) (1-cos(h))/h * lim(h->0) (1-cos(h)) = (0)(0) = 0 lim(x->π/2) cos(x)/cot(x) = lim(x->π/2) (cos(x)/1) * (sin(x)/cos(x)) = lim(x->π/2) sin(x) = 1 lim(x->0) (1-e^(-x))/(e^x-1) = lim(x->0) (e^x(e^x-1))/(e^x-1) = lim(x->0) e^x = 1 lim(t->0) sin(3t)/2t = lim(t->0) (1/2) * (3sin(3t)/3t) = 3/2 * lim(t->0) sin(3t)/3t = 3/2 * (1) = 3/2 107) s(t) = -16t² + 500 lim(t->a) (s(a) - s(t)) / (a - t) at a = 2 s(2) = -16(2)² + 500 = 436 lim(a->2) (-16a² + 500 - 436) / (a - 2) = lim(a->2) (-16a² + 64) / (a - 2) = lim(a->2) -16(a² - 4) / (a - 2) = lim(a->2) -16(a + 2)(a - 2) / (a - 2) = -64 VELOCITY AT 2 sec: -64 ft/sec = SPEED = 64 ft/sec (HOW FAST) 108) HITS GROUND? s(t) = 0 -16t² + 500 = 0 -16t² = -500 t² = 500/16 t = √(500/16) = (10√5)/4 = (5√5)/2 sec HITS GROUND AT (5√5)/2 sec ≈ 5.59052 sec at a = (5√5)/2 s((5√5)/2) = -16((5√5)/2)² + 500 = 0