, - or neither.1.
136.150: Test #220 minutes
Name:_____________________ Student Number: _______
1. Evaluate the following limits or show they do not exist. In the latter case check if the limit is , - or neither.
(a) 
(b) 
(c) 
(a) As x approaches 3 from the left hand side, the denominator x-3 approaches 0 through
negative values (while the numerator will stay close to 6). Consequently, the limit is
(and it does not exist).
(b) 
(c) 
2. Which of the functions 
and 
is (a) continuous, (b) right continuous, (c) left continuous at the point 
? Justify your answers.
; 
; 
. Since all these are equal, it follows that f(x) is continuous (from left, raght or both) at x=1.
; 
; 
. Since all these are not all equal, g(x) is not continuous at x=1. But, since 
the function g(x) is continuous from left at x=1.
3. Find an equation of the tangent and an equation of the normal to the curve 
at the point (recall that the normal to the curve at a given point is the line that is perpendicular to the tangent at that point).
The slope of the tangent line is
.
So the equation of the tangent line is 
.
The slope of the normal line is 
, ans so its equation is 
.