
Let

The curl is

where  denotes the partial derivative operator with respect to
 denotes the partial derivative operator with respect to  . Recall that
. Recall that



and that for any two vectors  and
 and  ,
,  , and
, and  .
.
The cross product reduces to

When you compute the partial derivatives, you'll find that all the components reduce to 0 and

which means  is indeed conservative and we can find
 is indeed conservative and we can find  .
.
Integrate both sides of

with respect to  and
 and

Differentiate both sides with respect to  and
 and




Now

and differentiating with respect to  gives
 gives




for some constant  . So
. So

 
        
             
        
        
        
Answer:
(You never showed the graphs we were suppose to choose from) 
The graphs of all exponential functions have these characteristics. They all contain the point (0, 1), because a0 = 1. The x-axis is always an asymptote. They are decreasing if 0 < a < 1, and increasing if 1 < a.
 
        
             
        
        
        
Answer: -2x^2 (3x^2 + 8)
Step-by-step explanation: a^b+c =a^b a^c
1) -16x^2 - 6x^ x^2
2) Rewrite -16 as -2 * 8
2.a Rewrite -6 as -2 * 3 
= -2 * 8x^2 - 2 * 3x^2x^2
3) facter out common term: -2x^2
= ur answer 
 
        
             
        
        
        
Answer:
(a)

(b)$2
Step-by-step explanation:
In the given game of rolling a die. these are the possible winnings.
- If the number showing is even(2, 4, or 6) or 1, you win $3.
- If the number showing is either 3 or 5 you win $0.
There are 6 sides in the die.

(i)The probability distribution of x.
Let x be the amount won
Therefore:
Probability distribution of x.

(ii) Expected amount of dollar won
Expected Amount
 
You would expect to win $2.
 
        
             
        
        
        
50 + 3(B) + 50 + 3(R) + 50 + 3(Y) would be the equation.