1. Use the ε-δ definition of continuity to prove that (a) f(x) = x 2 is...
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1. Use the ε-δ definition of continuity to prove that (a) f(x) =x 2 is continuous at every x0. (b) f(x) = 1/x is continuous atevery x0 not equal to 0.
3. Let f(x) = ( x, x ∈ Q 0, x /∈ Q (a) Prove that f isdiscontinuous at every x0 not equal to 0. (b) Is f continuous at x0= 0 ? Give an answer and then prove it.
4. Let f and g be two functions on R. Prove that if f and g arecontinuous on R and f(q) = g(q) for every q ∈ Q, then f(x) = g(x)for every x ∈ R.
1. Use the ε-δ definition of continuity to prove that (a) f(x) =x 2 is continuous at every x0. (b) f(x) = 1/x is continuous atevery x0 not equal to 0.
3. Let f(x) = ( x, x ∈ Q 0, x /∈ Q (a) Prove that f isdiscontinuous at every x0 not equal to 0. (b) Is f continuous at x0= 0 ? Give an answer and then prove it.
4. Let f and g be two functions on R. Prove that if f and g arecontinuous on R and f(q) = g(q) for every q ∈ Q, then f(x) = g(x)for every x ∈ R.
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