Calculus- Homework 3 Solved

Problem 1
(10 points)

a)     Compute the following limit lim  .           

b)    Find the asymptotes of the graph  .      

Problem 2


Find the limit of the following functions using ”Squeeze Law”.

a)      ) where n ∈N\{0}          

b)          

Problem 3
Show that the equation

cos(x) = ex + x + 2

has at least one solution over R.                                                                                                        

Hint : Intermediate value theorem.

Bonus: Prove that the function

f(x) = ex + x + 2

has only one root