Maths Quest Maths B Year 11 for Queensland Chapter 13 Differentiation and applications WorkSHEET 13.11
WorkSHEET 13.1Differentiation and applicationsName: ______
Maths Quest Maths B Year 11 for Queensland Chapter 13 Differentiation and applications WorkSHEET 13.11
1 / Evaluate the following limits:(a)
(b)
(c) / (a)
(b)
(c)
/ 1
1
1
2 / Evaluate the following limits:
(a)
(b) /
/ 1
1
1
1
3 / Evaluate the following limit: /
So
/ 1
1
4 / For what values of x is the function in
(a)question 2 (a) discontinuous?
(b)question 2 (b) discontinuous?
(c)question 3 discontinuous? / (a)is discontinuous when the denominator is undefined; that is,
when x = 2
(b)Similarly, is discontinuous when x = 2.
(c)
is discontinuous when
/ 1
1
1
5 / Investigate the following limit:
/ As x 2, 2 x 0
As x 2, 4 x0
As both parts of the function approach the same limit, the limit exists. / 1
6 / Investigate the following limit:
/ For
For
As both parts of function do not approach the same limit, the limit does not exist. / 1
7 / Find for each of the following:
(a)
(b) /
/ 1
1
8 / (a)What is the gradient of the straight line with equation:?
(b)Compare the answer to part (a) with the answer to the following limit:
What can you conclude? / (a) The gradient is equal to the coefficient of x, which is 4.
(b)
The same answer indicates that the expression in part (b) is an alternative way of deriving the gradient. / 1
1
1
9 / Use the limit to find an expression for the gradient for each of the following:
(a)
(b) / (a) 2
(b) 2
10 / Evaluate for each of the following:
(a)
(b) / (a) 2
So
(b) 2
So