MATH 281, Supplementary Calculator Exercises

 

1. Find the smallest positive solution of the equation
   
   .

 

2. Find all intersections of the graphs of
   
    and
   
    for
   
   .

 

3. Find the maximum of each function on the interval
   
   .  Plot the graph of each function over the given interval.
1. 
   
   .
2. 
   
   .

 

4. Use Simpson’s rule and the trapezoidal rule with 100 steps to estimate each integral.
1. 
   
   .
2. 
   
   .

 

5. Find each integral.
1. 
   
   .
2. 
   
   ,

 

6. Determine whether or not each of the following integrals converges.  Give the numerical value of each convergent integral.
1. 
   
   .
2. 
   
   .
3. 
   
   .
4. 
   
   .