Problem 1

1. Compute the following limit lim .
2. Find the asymptotes of the graph .

Problem 2

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

1. ) where n ∈N{0}

Problem 3

Show that the equation

cos(x) = e^x + x + 2

has at least one solution over R.

Hint : Intermediate value theorem.

Bonus: Prove that the function

f(x) = e^x + x + 2

has only one root