In this collection there is a number of questions: True or false? or Is it possi

Question

In this collection there is a number of questions: True or false? or Is it possible? Give a proof or an example in each case. Is it possible?

a) f is continuous at x0, g is not continuous at x0, and f + g is continuous at x0;

b) f and g are not continuous at x0, and f + g is continuous at x0; 2

c) f is continuous at x0, g is not continuous at x0, and f · g is continuous at x0;

d) f and g are not continuous at x0, and f · g is continuous at x0;

e) f is bounded, g is not bounded, and f + g is bounded;

f) f and g are not bounded, and f + g is bounded;

g) f is bounded, g is not bounded, and f · g is bounded;

h) f and g are not bounded, and f · g is bounded

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In this collection there is a number of questions: True or false? or Is it possi

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