Q1) find the limit of the function by using direct substitution.: limit as x approaches quantity pi divided by two of quantity three times e to the x times cosine of x. q2)find the limit of the function by using direct substitution: limit as x approaches zero of quantity x squared minus one. q3)find the limit of the function algebraically: limit as x approaches zero of quantity x squared plus three divided by x to the fourth power. answer asap u so much! this is super important!

Q1)
For the first question, the function is 
                                  f(x)=3eˣ * cos(x)
Now, 
         
By direct substitution of π/2,
we get,
         =    , as cos(π/2)=0
         = 0 

Q2)
For the second question, the function is 
                         f(x)= x²-1
Now,
           
By direct substitution,
         the square term will be zero and the answer is -1
            = 0 -1
            =-1
Q3)
For the third question, the function is
                                     f(x)=x²+3/x⁴
Now,
                       
                =  
Now, by using the property of limit separate the limit with both x² and 3/x⁴
the x² term will be zero and the second term will approach infinity.
                = 
                = infinity   is the correct answer.

         
                        

Are we assuming that we are using an eight of a cup of pumpkin puree per latte?
If we are then the answer would be 1.042 cups of milk more than puree.

First we have to find out how much puree we are using.
That would be ( 1/8 ) × 5 = 0.125 × 5 = 0.625 cups of puree.
Then we would find how much milk we are using.
That would be ( 2/3 ) × 5 = 0.666666 ( a lot of sixes ) × 5 = 1.666666 ( a lot of sixes ).
To find the difference, you would then have to subtract the amount of puree from the amount of milk.
You would get 1.666666 − 0.625 = 1.0416666 ( also a lot of sixes ). If you are doing this with your own calculator you should get approximately the same number.
Since the number isn't exact you can round up all the sixes to the nearest thousandth. You should get approximately 1.042 cups.
I hope this helped.