GRE 9367 42 and 64
Posted: Fri Sep 25, 2009 9:30 am
Need some help figuring out how to solve the following problems
42. What is the greatest value of b for which any real value function f that satisfies the following properties must also satisfy f(1)<5?
(i) f is infinitely differentiable on the real numbers
(ii) f(0)=1, f'(0)=1, and f''(0)=2; and
(iii) |f'''(x)|<b for all x in [0,1]
a. 1
b. 2
c. 6
d. 12
e. 24
64. Let V be the real vector space of all real-valued functions defined on the real numbers and having derivatives of all orders. If D is the mapping from V into V that maps every function in V to its derivative, what are all the eigenvectors of D?
a. All nonzero functions in V
b. All nonzero constant functions in V
c. All nonzero functions of the form ke^(lk), where k and l are real numbers
d. All nonzero functions of the form sum from i=0 to k of c sub i times x^i where where k>0 and csub i's are real numbers
e. There are no eigenvectors of D
the answers are d and c any help is greatly appreciated
42. What is the greatest value of b for which any real value function f that satisfies the following properties must also satisfy f(1)<5?
(i) f is infinitely differentiable on the real numbers
(ii) f(0)=1, f'(0)=1, and f''(0)=2; and
(iii) |f'''(x)|<b for all x in [0,1]
a. 1
b. 2
c. 6
d. 12
e. 24
64. Let V be the real vector space of all real-valued functions defined on the real numbers and having derivatives of all orders. If D is the mapping from V into V that maps every function in V to its derivative, what are all the eigenvectors of D?
a. All nonzero functions in V
b. All nonzero constant functions in V
c. All nonzero functions of the form ke^(lk), where k and l are real numbers
d. All nonzero functions of the form sum from i=0 to k of c sub i times x^i where where k>0 and csub i's are real numbers
e. There are no eigenvectors of D
the answers are d and c any help is greatly appreciated