#### MATH 16A

##### Midterm 1 | Winter '14| Glaros
Q1]...[20 points] Compute the following limits:
a)

b) (HINT: multiply by the conjugate before taking the limit.)

Q2]...[20 points]
a) Write the three conditions for a function $y = f(x)$ to be continuous at a point $x = a$.

b) Using the three conditions above, determine whether the following function is continuous at the point $x = 2$

Q3]...[20 points]
a) Write the limit definition for the derivative of a function $y = f(x)$.

b) Compute $f'(x)$ using your limit definition above for the function $y = \frac{1}{x^2}$.

Q4]...[20 points] Find all the points on the graph of with tangent lines to the graph of f parallel to the line $3y - 6x = 7$.

Q5]...[20 points] Compute the following derivatives:
a)

b) $y = \frac{15x^3}{1 - x^4}$