Prove using the definition of the limit that \lim_{x\rightarrow 4} \sqrt{x+5}=3lim x→4 x+5 =3. You need to find \deltaδ in terms of \epsilonϵ so that if |x-4|<\delta∣x−4∣<δ then |(\sqrt{x+5}-3|<\epsilon∣( x+5 −3∣<ϵ. g

Do some research and find a city that has experienced population growth. determine its population on january 1st of a certain year. write an exponential function to represent the city’s population, y, based on the number of years that pass, x after a period of exponential growth. describe the variables and numbers that you used in your equation.

What is the expression in factored form? 3x^2 + 18x + 24 a. 3(x+2)(x+4) b. 3(x-2)(x+4) c. 3(x-2)(x-4) d. 3(x+2)(x-4)

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (–4, 0) and (6, 0). the y-intercept of the first parabola is (0, –12). the y-intercept of the second parabola is (0, –24). what is the positive difference between the a values for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth