Question

real analysis (a) prove that e^x is continuous at x=0 (b) using (a) prove that it...

real analysis

(a) prove that e^x is continuous at x=0
(b) using (a) prove that it is continuous for all x
(c) prove that lnx is continuous for positive x

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove that there is a positive real number x such that x2 - 2 = 0....
Prove that there is a positive real number x such that x2 - 2 = 0. What you'll need: Definition of a real number, definition of positive, definition of zero, and definition of Cauchy.
a. Assume E[X] is finite for a non-negative continuous random variable X. Prove that 1 −...
a. Assume E[X] is finite for a non-negative continuous random variable X. Prove that 1 − Fx (a) ≤ E[X]/a . b. Assume the MX(t) exists for a continuous random variable X. Prove that 1−Fx(a)≤ Mx(t)/eta
Prove the following using the specified technique: (a) Prove by contrapositive that for any two real...
Prove the following using the specified technique: (a) Prove by contrapositive that for any two real numbers,x and y,if x is rational and y is irrational then x+y is also irrational. (b) Prove by contradiction that for any positive two real numbers,x and y,if x·y≥100 then either x≥10 or y≥10. Please write nicely or type.
28.8 Let f(x)=x^2 for x rational and f(x) = 0 for x irrational. (a) Prove f...
28.8 Let f(x)=x^2 for x rational and f(x) = 0 for x irrational. (a) Prove f is continuous at x = 0. (b) Prove f is discontinuous at all x not= 0. (c) Prove f is differentiable at x = 0.Warning: You cannot simply claim f '(x)=2x.
Let f : [a,b] → R be a continuous function such that f(x) doesn't equal 0...
Let f : [a,b] → R be a continuous function such that f(x) doesn't equal 0 for every x ∈ [a,b]. 1) Show that either f(x) > 0 for every x ∈ [a,b] or f(x) < 0 for every x ∈ [a,b]. 2) Assume that f(x) > 0 for every x ∈ [a,b] and prove that there exists ε > 0 such that f(x) ≥ ε for all x ∈ [a,b].
prove that f(x) = sin(x^2) is continuous, positive and decreasing
prove that f(x) = sin(x^2) is continuous, positive and decreasing
Real Analysis: Suppose f: [0,1] --> R is continuous, and {xn} is a Cauchy sequence in...
Real Analysis: Suppose f: [0,1] --> R is continuous, and {xn} is a Cauchy sequence in [0,1]. Prove or disprove that {f(xn)} is a Cauchy Sequence.
Part I) Prove that if f and g are continuous at a, then f+g is continuous...
Part I) Prove that if f and g are continuous at a, then f+g is continuous at a using the epsilon-δ definition. Part II) Let a, L ∈ R. Prove that if a ≥ L− ε for all positive, then a ≥ L.
Prove that the integral from 0 to Infinity (sin^2(x)e^-x)dx converges using the comparison test.
Prove that the integral from 0 to Infinity (sin^2(x)e^-x)dx converges using the comparison test.
Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that...
Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that if f(x) > 0 only on a single (possibly infinite) interval of the real numbers then F(x) is a strictly increasing function of x over that interval. [Hint: Try proof by contradiction]. (b) Under the conditions described in part (a), find and identify the distribution of Y = F(x).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT