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

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