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(a) Determine whether each of the following functions is uniformly continu- ous on the given domain....
The functions fand g are given. Find each of the following functions and determine their domain. (Enter your answer for each domain using interval notation.) (x) = 3x + 4 and g(x)=2x-3 (a) (f+)x) function (f+)() - domain (b) (- 9)x) function (f - 9)x) = domain C) (f. 9x) function (f)(x) = domain function domain
3. For each of the following functions, (i) Determine the domain, (ii) Find their first derivatives, (iii) Find their second derivatives, (iv) Determine whether they are globally concave? Why or why not? (a) f(x) = 4x? - (b) f(x) = ln(22 - 2) (c) f(x) = e
For each of the following functions, determine whether or not they are (i) one-to-one and i) onto. Justify your answers (a) f : R-{0} → R and f(x) = 3r-1/x (b) g : R _ {1} → R and g(x) = x + 1/(x-1) (c) l : S → Znon-reg and l(s) = number of 1's in s, for all strings s E S, where s is the set of all strings of O's and 1's. (d) 1 : S...
Finding the Domain of Radical Functions Determine the domain for each of the following functions. Write your answer in Interval Notation and as an Inequality. Radical Function Domain written in Interval Notation Domain written as an Inequality 1 2 f(3) = V160 - 18 9(2) = 107–13. - 16 f(x) = - 17 + 174 + 12 p(x) = v=3 + 10% DE VIDA
With justification in each one. Clarification; why if true and why if false? Please Determine whether the following statement is true or false: • Iff: R+R is differentiable and strictly increasing on R, then f'(1) > 0 VI ER • If S: R R is continuous and f(x) - ron Q, then (V3) - 3. • If f,g: (0,1) - Rare functions such that \S(1)-f(y) = g(1)-9(y) for all 1, y € (0, 1) and g is continuous on (0,1),...
- In each part, determine whether the pairing (, ) determines an inner product on the vector space V. Justify your answer. (1) V=R>, <[ 3 ][ ==x". (ii) V = R", (7,w) = tr((AU) Aw) where t denotes transpose and A is an invertible matrix. (iii) V =R”, (7,w) = tr((AT)* Aw) where t denotes transpose and A is a non-invertible matrix. (iv) V = C([0,1],R), (f(x),g(x)) = 5o+ f(x)g(x)dx.
2. Determine whether the given sets are countable or uncountable. Justify each answer with a bijection (or table like we did with Q+) or using results from class/textbook. (a) {0, 1, 2} * N (b) A = {(x, y) : x2 + y2 = 1} (c) {0, 1} R Che set of all 2-element subsets of N (e) Real numbers with decimal representations consists of all 1s. (f) The set of all functions from {0,1} to N
9. For each of the following pairs of functions, determine the highest order of contact between the two functions at the indicated point ro: (a) f,g :R-R given by f(x)-cos a and g(xo0 (b) f,g RR given by f(x) coS and g(x) 1 - j; ro0. (c) f,g:R-R given by f(x)-sinr and g(x0 (d) f,g:R-R given by f(x) sinz and ga)0. (e) f, g : R → R given by f(x)-e*2 and g(x)-1+z?: zo = 0. (f) f, g :...
2. Sketch the graph of each of the following functions, and determine whether the given function is one-to-one. Show your work! (a) f(x) = -|x +31 – 2 (b) g(x) X + 3 X + 2
Consider the functions F and Gas shown in the graph to the right Find the domain of the domain of G, and the domain of F. What is the domain of F? (Type your answer in interval notation) YA Total profit is defined as total revenue, R(x), minus total cost. Cix), and is given by the function PRO-COX). Given Rx)=5&x-0322 and Codex + 15, find each of the following a) PIX) b) R(100), C(100), and P(100) P(x)=0 (Type in descending...