6. Suppose f and g are functions with domain R. If both f and g are even but f+g is odd, then prove that g(x) = -f(x) for all r ER. %3D 7. Suppose neither lim f(x) nor lim g(x) exists. Show that lim...

Extracted text: 6. Suppose f and g are functions with domain R. If both f and g are even but f+g is odd, then prove that g(x) = -f(x) for all r ER. %3D 7. Suppose neither lim f(x) nor lim g(x) exists. Show that lim f(x)g(x)] may exist. x – 4 8. Prove that lim Va = 2 using the e-d-definition. Hint: Va - 2 = %3D VI +2 9. Suppose g is a function continuous at c and g(c) > 0. Prove that there exists 8>0 such that g(x) >0 for all r E (c- 8, c+ 8). 10. Consider the function if r E Q f (x) = if x Q. Prove that f'(0) = 0. Hint: The fact stated in Question 10 of Problem Set 2 is useful.