Each natural number n, 1)Show that, for each natural number

Each natural number n

Reference no: EM13760476

1)Show that, for each natural number n, the function f_n(x) = x^(1/n) has derivative f_n ' (x) = 1/n x ^ (1/n - 1) for x not equal to 0.

2)Show that, for each real number b>0, the function f(x) = b^x (defined by b^x = sup{b^r, r rational, r<=x}) is differentiable for all real x, with f'(x) = C b^x for some constant C (no need to compute this constant exactly).

Reference no: EM13760476

Questions Cloud

The past half century has seen dramatic changes in families : The past half century has seen dramatic changes in families in the United States. List some of the changes, tell whether you think they will continue in the future, and speculate on the cultural changes that you think may result.

Enterprise impact and measurement of business intelligence : Write a summary of the discussion your team had about enterprise impact and measurement of business intelligence.

What are some key intellectual property protections : What are some key intellectual property protections, if any, that your company possesses. When do these protections (e.g., patents) expire. How does your company intend to recoup lost revenues due to any patent or other intellectual property prote..

Prove that y(t) is a poison process with parameter ?p : Let {X(t), t ≥ 0} be a Poisson process with intensity parameter λ. Suppose each arrival is "registered" with probability p, independent of other arrivals. Let {Y(t), t ≥ 0} be the process of "registered" arrivals. Prove that Y(t) is a Poisson process..

Each natural number n : 1)Show that, for each natural number n, the function f_n(x) = x^(1/n) has derivative f_n ' (x) = 1/n x ^ (1/n - 1) for x not equal to 0.2)Show that, for each real number b>0, the function f(x) = b^x (defined by b^x = sup{b^r, r rational, r

Write the binomial probability function : A. A restaurant has found that about 20% of the diners with reservations do not show up. Suppose that 12 reservations parties are made. a) Write the binomial probability function for this experiment.

The plurality method which states : Talk about a real-world example using the Plurality Method which states that the candidate with the most first-place votes wins the election, to decide an election.

The total weight of bean : The beans are selling for $0.80, $1.20, and $1.80 per pound. You want to know how much of each grade of bean to buy, based on the following assumptions given to you by the owner: The total weight of beans needed is 15,000 pounds to minimize shippi..

A homogeneous poisson process with parameter : Let X(t) be a homogeneous Poisson process with parameter λ. Determine the covariance between X(t) and X(t + τ), t>0 and τ >0, i.e., compute E[(X(t) -E(X(t))(X(t + τ) - EX(t + τ))].

User Account

All Pages