#1
- The limit tends to 0
- Hence c=0
- Here limit tends to 1
- Hence c=1
- Here x tends to infty.
- c=infty
For the fourth one limit also tends to zero
The Lagrangian,
has critical points where its partial derivatives vanish:
tells us 
, so that
Then with 
, we get
and 
tells us
Then there are two critical points, 
. The critical point with the negative 
-coordinates gives the maximum value, 
.
<u>Answer</u>
9+√14
<u>Explanation</u>
To Rationalize the denominator of 5-√7/9-√14.
To rationalize this we multiply both the denominator and denominator by the conjugate of the denominator.
The denominator is 9-√14 and its conjugate is (9+√14).
(5-√7)/(9-√14) = (5-√7)(9+√14)/(9-√14)(9+√14)
= (5-√7)(9+√14)/(9²-14)
= (45 + 5√14 - 9√7 - √98)/(81-14)
= (45 + 5√14 - 9√7 - √98)/67
= (45 + 5√14 - 9√7 - 7√2)67
This is the rationalized expression.
The denominator is (9-√14) and its conjugate is (9+√14).
Answer:
5.) b = -2/5 (or -0.4 in decimal form)
6.) 20.5
