Answer:
b. 1/2
Step-by-step explanation:
lim        (x -3)(x +2) 
x-->-∞    ---------------
               2x^2 + x +1 
= lim        (x^2 -3x +2x - 6) 
x-->-∞    -----------------------
               2x^2 + x +1 
= lim        (x^2 -x - 6) 
x-->-∞    -----------------------
               2x^2 + x +1 
When we plug in x = -∞, we get indeterminate form.
Now we have to use the L'hospital rule.
d/dx (x^2 - x - 6) = 2x -1
d/dx (2x^2 + x + 1) = 4x + 1
Now apply the limit
lim            (2x - 1) / (4x + 1)
x--->-∞ 
Here we have to degree of the numerator and the denominator of the same. In this case, if x --> -∞, we get the result as the coefficient of the leading term as the result.
According to the rule, we get
= 2/4
Which can simplified as 1/2
The answer is 1/2
Hope this will helpful.
Thank you.
 
        
                    
             
        
        
        
X = 30 I think as angle on straight line = 180 so 180-103 = 77 , 30+43 = 73 , 77+73 = 150 , 180-150= 30 , then opposite angles are the same so therefore x = 30 degrees
        
             
        
        
        
The answer is 54 square units.
let the vertex in quadrant I be (x,y) 
<span>then the vertex in quadratnt II is (-x,y) </span>
<span>base of the rectangle = 2x </span>
<span>height of the rectangle = y </span>
<span>Area = xy </span>
<span>= x(27 - x</span>²<span>) </span>
<span>= -x</span>³<span> + 27x </span>
<span>d(area)/dx = 3x</span>²<span> - 27 </span><span>= 0 for a maximum of area </span>
<span>3x</span>²<span> = 3 x 3</span>² = <span>27 </span>
<span>x</span>²<span> = 9 </span>
<span>x = ±3 </span>
<span>y = 27-9 = 18 </span>
So, the largest area = 3 x 18 = 54 square units
        
                    
             
        
        
        
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