Final review (Spring 2021) 1. Find the limit of the following sequence when n o: an = 2-n+3n2 n-3n+6 2. Find the vertical and horizontal asymptotes of the function f(x)= 3. Find the derivative of the function f(x) = xe- 2x-8 x -2x 4. Find the points of local maximum, local minimum and inflection points of the function f(x)=x-6x+9x-4 5. Find the definite integral: [(3x-x+1)dx -2 6. How many 3-digit numbers (from 100 to 999) have all different digits and do not contain even digits? (0 is considered an even digit). 7. Two vertices of the regular octagon (a polygon with 8 sides) are picked at random. Find the probability that the segment connecting them is NOT the side of the octagon. 8. Two dice are rolled several times. What is the probability that for the first time the sum of the outcomes will be greater or equal 10 on the 3rd attempt? 9. A random variable X is given by its distribution function F(x): F(x)=0, if -