Limits and continuity

2000018703

Level: 
B
The picture shows a graph of a function. Decide at which of the marked points \(x_1\), \(x_2\), \(x_3\) and \(x_4\), the left-hand and right-hand limit of the function has the same value. (Note: The dashed lines are asymptotes of the function.)
Only at \(x_1\) and \(x_3\).
Only at \(x_1\).
Only at \(x_3\).
The left-hand and right-hand limit is the same at any marked point.

2000018702

Level: 
B
Choose the true statement about the limits of the function whose graph is shown in the picture. (Note: The dashed lines are asymptotes of the function.)
The function has the limit "negative infinity" only at \(x_2\) and at "negative infinity" it has the limit \(a_2\).
The function has the limit "negative infinity" at \(x_2\) and \(x_3\) and at "negative infinity" it has the limit \(a_2\).
The function has the limit "negative infinity" only at \(x_2\) and at "negative infinity" there is no limit.
The function has the limit "negative infinity" at \(x_2\) and \(x_3\) and at "negative infinity" there is no limit.

2000018701

Level: 
B
The following pictures show graphs of \(3\) functions. Choose the true statement about the limit at \(x = 3\).
The functions \(f\), \(g\), \(h\) have the same limit at \(x = 3\).
The function \(g\) has no limit at \(x = 3\).
The function \(f\) has no limit at \(x = 3\).
The limits of functions \(f\), \(g\), \(h\) at \(x = 3\) differ.
Only the function \(h\) has a limit at \(x = 3\).