Let f: [a, b] → r be a continuous function. let ε > 0 be a constant. for x [a + e, b-el, define g(x) : = (a) show that g is differentiable and find the derivative. (b) let f be differentiable and fix x e (a, b) (lete be small enough). what happens to g'(x) as ε gets smaller? (c) find g for f(x) : = lxle = 1 (you can assume [a, b] is large enough).

Which values for a and b will create infinitely many solutions for this system of equations? ax-y=8 2x+y=b

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60

Aline that intersects one of two parallel lines intersects the other also always sometimes never