1. For the followings, find whether limit exists? If it does, find its value. (a) Find Lim X 2-X-6 X → -2 X+2 (6 points) (b) Find Lim 3X 3-X-6 X →∞ X4+2 (4 points) (c) Find Lim X 2-10X-6 X →-∞ 100X+2 (4 points)2)Check the continuity of the following functions.(a) Y= 3X2-7X- 6 in closed interval [-10, 50] (6 points) X+5 (b) 2-X if X 5 3. (a) Find the point where the slope of f(X) = 5X – lnX is (-5) (10 points) (b) Find the first derivative of X – 1/X2 (FROM FIRST PRINCIPLE) (10 point4)Differentiate (4 x 5 = 20 points)(a)f(x) = (√ x +1)(x(2/5)+3x)(b)f(x) =(5×3+1)/(x2+2x+1)(c)f(x) = -5x(3x-3)4(d)f(x) = (2x + (x2+x)4)(1/3)5 )Solve the following equations (2 x 5 =10 points)1. 8e5t. = 252. ln (x+1) – ln (5-x) = ln 96) Carbon-14 has a half-life value of 5800 year. How old is the pyramid if a piece of wood found at pyramid side has lost 60% of its carbon-14? (10 points)7)Differentiate (2 x 5 =10 points)a)4x . log 2 5x ( 2 is the base of log)b)9x/(x5+2x+3)
