Reference no: EM13192432

1. f(x) = 2x^3 over interval [1,3]. what is f'(x) according to mean value theorem?

2. A function f is continuous on interval [1,3]. A horizontal line is drawn somewhere between the lines y=f(1) and y=f(3). According to the intermediate value theorem, how many times is such a line guaranteed to intersect the graph of f(x)?

3. A circle's radius is increasing at a rate of 1.5 meters per second. At what rate is the circle's area increasing when the radius is 2.5 meters?

4. A rectangular plot of land is to be bounded on one side by a river and on the other 3 sides by a wire fence. If there are 800 feet of fencing available, what is the maximum possible area the plot can have?

5. Suppose that the function f(x) is defined on an open interval about x sub 0 = 5. Also suppose that for every number b>0, there exists a corresponding number a>0, such that for all values of x in the interval, if 0<absolute value of x-5<a, then absolute value of f(x) -7 <b. What are two possible answers?

6. limit as x approaches (-1) of -2x^3 + 4x + 1. Evaluate the limit

7. limit as x approaches theta of (sin theta cos(theta + pi/2)^theta)/theta. Evaluate the given limit.

8. limit as x approaches infinity of 1/(ln x^2-3). Evaluate the limit.

9. Let f(x) = (x-2)/(x^2 -4). Evaluate lim as x approaches 2 of f(x).

10. lim as x approaches 0 of (cos x - 1)^2/sin x. Evaluate the above expression using L'Hopital's rule.