These problems are real analysis related problems. One of these is Liptuaz continuity/holder condition. It would be nice if you use mean value theorem for solving that problem.
1. Let f : [0, 2] ? R be continuous, assume that f is twice differentiable at all points of (a, b), and assume that f(0) = 0, f(1) = 1 and f(2) = 2. Prove: There exists c ? (0, 2) such that f??(c) = 0.
2. Let f : (a, b) ? R, where a, b ? R and a < b and suppose f is monotone. Prove lim x?c+ f(x) and lim x?c? f(x) exist at all c ? (a, b).
3. Let f : [0, 1] ? R be continuous, differentiable at all points of (0, 1). Assume f?(x) ? 16 for all x ? (0, 1). Prove there is some interval J ? [0, 1] of length 1/4 such that |f(x)| ? 4 for all x ? J.
4. Let I be an open interval in R, f : I ? R and suppose that f satisfies the following condition: There exist constants C and ?, C > 0 and ? > 1, such that |f(x) ? f(y)| <C|x ? y|?for all x, y ? I. Prove: f is constant. (A function that satisfies a Holder condition of order ? with ? > 1 is a constant.)© BrainMass Inc. brainmass.com October 25, 2018, 5:53 am ad1c9bdddf
This solution clearly assesses real analysis. Differentiability in real analysis are solved.
Regression model for real estate data
Refer to the data included in the Excel file, which report information on homes sold in the Somewhere, USA, during a recent year. Use the selling price of the home as the dependent variable and determine the regression equation with number of bedrooms, size of the house, whether there is a pool, whether there is an attached garage, distance from the center of the
city, and the number of bathrooms as independent variables.
i) Construct a 95% confidence interval estimate of the population slope between selling price and each of the following variables: number of bedrooms, size in sq. ft., distance to CBD, and number of bathrooms.
j) Compute and interpret the coefficients of partial determination.
k) Predict the selling price of a 2,500 square feet house that has 5 bedrooms, 3 bathrooms,
a 3-car attached garage, no pool, and is at 18 miles from the city center.
l) Rerun the analysis until only significant regression coefficients remain in the analysis. Identify these variables.