Applied calculus quiz

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 < 0

Y= X²-5X+2 if 0 < X < 5 (10 points)

6 – (10/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 point

4)Differentiate (4 x 5 = 20 points)

(a)f(x) = (? x +1)(x^(2/5)+3x)

(b)f(x) =(5x³+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. 8e^5t. = 25

2. ln (x+1) – ln (5-x) = ln 9

6)

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)4^x . log ₂ 5^x ( 2 is the base of log)

b)9^x/(x⁵+2x+3)