Page 271 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes Polynomial Function: A function of the form y = a + a x + a x + .................. .......... + a x n
2
0 1 2 n
Rational Function: The ratio of two polynomial functions.
Successive Differentiation: The process of finding higher ordered derivatives is called successive
differentiation.
Variable: A quantity whose value changes.

9.8 Self Assessment

x
( d e 2 –5 )
1. Find value of
dx
(a) 2e 2x – 5 (b) 2e 2x + 5
(c) 2x ex – 5x (d) 2x + e 2x – 5

d
2. Find value of log(4x 5)
dx
4 2
(a) (b)
4x 5 2x 5
4x 4x 2
(c) (d)
4x 5 4x 5
2
d y
,
3. Find 2 if xy + 4y = 4x
dx
5( – 4) 5(y 4)
y
(a) 2 (b) 2
x
(x 4) ( – 4)
y
4( – 4) 4(y 4)
(c) 2 (d) 2
x
x
( – 4) ( – 2)
2
d y
2
4. Find 2 if y = (x + 2)log x
dx
2 2
(a) 3 + 2 log x – 2 (b) 2 + 3 log x – 2
x x
2 2
(c) 2 – 3 log x – (d) 3 – 2 log x –
x 2 x 2
Fill in the blanks:
2
n
5. A function of the form y = a + a x + a x + ................... + a x is called as ...................
0 1 2 n
6. The ratio of two polynomial functions is called ...................
7. ................... is a function which is expressed as a root of a polynomial.
9.9 Review Questions

1. Find domain and range of the following functions:

x 3 a 3 1
(i) y (ii) y x 2
x a x

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