Homework 6
Please complete the homework before the tutorial class and prepare to present in the tutorial
class.
Question 1
Find the following limits
2x + 1 − 4 x2 + 9
x →2
x−2
i.
lim
ii.
lim
x →
4 x 2 + 3x − 1
3x − 2
1
Question 2
2e x −1 + x
, x 1
at x = 1
Check the continuity of f ( x ) = 
3x + ln ( 2 x − 1) , x  1
Question 3
2
Find equations of tangent and normal to the curve defined by f ( x ) = 3xe x −1 at x = 1
2
Question 4
Find and simplify the derivative of the following functions
2 − 3x 2
3x + 1
i.
f ( x) =
ii.
f ( x ) = ln ( e x + cos ( x ) )
iii.
f ( x ) = 3x − 1 + 2 x
3