Question

2.
$\frac{1 + x + \frac{x {}^{2} }{4} }{1 - \frac{x {}^{2} }{4} }$
... '

​

Answer 1

For x>0 you have

x+1x−2=x2x+1x−2xx=x2−2x+1x=(x−1)2x≥0

Step-by-step explanation:

Consider the function

f(x)=x+1x

Its first derivative

f′(x)=1−1x2

cancels for x=1 and f(1)=2 is then an extremum. Its second derivative is

f′′(x)=2x3

is positive. Then x=1 corresponds to a minimum and the inequality is always satisfied.

Answer 2

Step-by-step explanation:

As Tyl was a Flemish painter, the Captain of Guards allowed him to meet the

Archduke. The Archduke welcomed him. He gave him a grand feast. Tyl presented his

painting to the Archduke. The Archduke was impressed and Tyl was appointed as the

court painter. Tyl was thrilled. That night he was so excited that he could not sleep. He

expressed his feelings in his diary. Prepare the possible diary entry.

Points to remember while writing a diary.

• Day/ date

15 |

Proper initiation with an expression. (E.g. An unforgettable day) Alas!)

Recall the story and fix important events.

Use first person narrative.

Express feelings and thoughts of the character.