**Name:**

1. Determine the following limits (8 pts. each):

(a): lim_{x® 3-}[(x^{2}+5)/(x^{2}-9)] =

(b): lim_{x® 4}[(2x^{2}-9x+4)/(x^{2}-x-12)]=

(c): lim_{x® 5}[(3-[Ö(2x-1)])/(x-5)]=

2. Let f(x) = 2x^{4}+x^{2}-x-7.

Show that f(x) has at least one root somewhere on the real line. (15 pts.)
(Hint: Try to find one somewhere between, oh, I don't know, -3 and 3!
Trust me, you can't tell me
__what__ the root is, just that there
__is__ one!)

3. (a): Find, using (one of) the (limit) definitions of the derivative, the derivative of the function

at the point x=1. (15 pts.)

(b): Find the equation for the tangent line to the graph of y=f(x)=3x^{2}-5x+6 at the point (1,f(1)). (8 pts.)

4. Find, using any method, the derivatives of the following functions (7 pts. each):

(a): f(x) = 3x^{5}-6x^{[3/4]}+[5/(x^{2})]

(b): f(x) = (x^{2}+x+2)(3sinx -5)

(c): f(x) = [(x^{4}+3)/(2x^{3}-4x)]

(d): h(x) =sin(x^{[1/3]}-x)

5. Find the slope of the tangent line to the graph of the equation

at the point (2,1). (10 pts.)

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