Use the squeeze theorem; if
1 - <em>x</em> ²/4 ≤ <em>u(x)</em> ≤ 1 + <em>x</em> ²/2,
then taking the limit on each part as <em>x</em> approaches 0 gives
1 ≤ lim [<em>x</em> → 0] <em>u(x)</em> ≤ 1
and so the limit of <em>u(x)</em> as <em>x</em> → 0 is simply 1.
Given :
7x is an odd integer.
To Find :
The next odd integer as an algebraic expression in x.
Solution :
All positive integers are :
1 , 2 , 3 , 4 , 5 , ......
From the above series we noticed that every other odd number is 2 more than the previous one.
So , 7x is an odd number.
Therefore, next odd number is 7x + 2.
Hence, this is the required solution.
The next three terms of -243, 81, -27, 9 is
The given series is geometric series
<u>Solution:</u>
Given, series is -243, 81, -27, 9, …
We have to find the next three terms of the above given series.
Now, the given series can also be written as

We can say that, above series is in Geometric Progression with first term = -243 and common ratio = 
Then, next three term would be,

Hence, the next three terms of given G.P series are
<span>We can use the proportion. We already know that Dixon is 6 ft tall and that his shadow is 9 ft long. Also we know that the shadow of his sister is 6 ft long. 6 : x = 9 : 6, or 6 / x = 9 / 6. After that we will cross multiply : 9 * x = 6 * 6, 9 x = 36 , x = 36 : 9, x = 4. Answer: Ariadne is 4 feet tall.Hope I helped! :) Cheers!</span>
An estimate here would be 73,500+ 28,000= 101,500 but the actual answer would be 101,269