7.04.03

A1

TEST I

Task 1 (10p.) Evaluate the following limits

a )
; b)

Task.2 (10p.) Evaluate the limits of the following functions (do not use derivatives)

a)
; b)

Task 3 (6p.) Use the Intermediate-Value theorem to show that the equation

has a solution in the interval
.

Task 4(7p.) Determine such values of the parameters

and
that the function

is continuous in R.

Task 5 (10p) Determine the convergence or divergence of the following series:

a)

; b)
.

Task.6 (7p.) Formulate the Limit-Comparison Test and use it to determine the convergence or divergence of the series
.

.