Math 161

Sample Midterm 1

Solution to problem 1

Dr. Wilson

1. Find

when

We have some algebra to do to simplify the right side of this equation. We are subtracting fraction in the numerator, so we need common denominators.

We are now ready to invert the bottom and multiply.

When we do, we can reduce the fraction. Our final result is continuous when h = 0, so the limit is obtained by simply substituting a 0 in for h.

 

Note that this gives you the same result we would get if we applied the power rule to the problem.