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Basic Mathematics – I

Notes When x –7–, we have 2x – 1 –15 < 0 and x + 7 0 and x + 7 < 0, so:

Thus doesn’t exist.

The line y = 2 is the horizontal asymptote. The line x = –7 is a vertical asymptote.
5. Find any horizontal and vertical asymptotes of each of the following functions.

(a) for all x > 2.

(b) for all x > 2.

(c) for all x 2

Solution

(a)

the horizontal asymptote of f is the x­axis.

the vertical asymptote of f is the line x = 2.
(b)

the horizontal asymptote of g is the x­axis.

the vertical asymptote of g is the line x = 2.
(c)

a horizontal asymptote of h is the x­axis;

7.6 Basic Theorems of Limits

1.

To verify this, consider the function f(x) = 5x.
We observe that in , 5 being a constant is not affected by the limit.

=

=

where g(x), h(x), P(x), ..... are any function.

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