Description

Problem 1
(10 points)
a) Compute the following limit lim . (5 points)
b) Find the asymptotes of the graph . (5 points)
Problem 2
(10 points)
Find the limit of the following functions using ”Squeeze Law”.
a) ) where n ∈N{0} (5 points)
b) (5 points)
Problem 3
(10 points)
Show that the equation
cos(x) = ex + x + 2
has at least one solution over R. (10 points)
Hint : Intermediate value theorem.
Bonus: Prove that the function
f(x) = ex + x + 2
has only one root (5 points)