Page 222 - DMTH201_Basic Mathematics-1

Unit 7: Limits

Notes
Figure 7.3 Figure 7.4

y y

0 (0, 1)
x′  3 x
  2, 
2 

x′ 0 x = 1 x
y′

(ii) LHL

RHL

Further and

Thus function has x-axis as a horizontal asymptote and x = 1 is the vertical asymptote.
The graph of the function is shown in Figure 7.4.

(iii) Let This function implies that

y = when

= when

Hence (Horizontal asymptote).

Example 7:
A right-angled triangle has two equal sides of 1 inch. One of these sides, drawn horizontally, is
divided into (n + 1) equal portions. On each of the portion after the first a rectangle is formed with
height equal to the vertical distance from the left-hand end of the portion to the hypotenuse of the
triangle. Find an expression for the sum of rectangle areas and evaluate the limit of the sum as
n → ∞. What is the meaning of the limiting value?

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