1. Limits and Continuity

Determine the interval(s) for which the function is continuous.

$f\left(x\right)=x^2+4x-12$

Determine the interval(s) for which the function is continuous.

$f(x)=\frac{sinx}{(2+cosx)}$

Determine the interval(s) for which the function is continuous.

Suppose f(x) = {x^2 − 5x + 6 / x − 3 if x≠3

a if x=3.

Determine a value of the constant a for which lim x→3 f(x) = f(3).

Which of the following functions are continuous for all values in their domain? Justify your answers.

a. a(t)=altitude of a skydiver t seconds after jumping from a plane

Which of the following functions are continuous for all values in their domain? Justify your answers.

b. n(t)=number of quarters needed to park legally in a metered parking space for t minutes

Which of the following functions are continuous for all values in their domain? Justify your answers.

c. T(t)=temperature t minutes after midnight in Chicago on January 1

Which of the following functions are continuous for all values in their domain? Justify your answers.

d. p(t)=number of points scored by a basketball player after t minutes of a basketball game

Determine the points on the interval (0, 5) at which the following functions f have discontinuities. At each point of discontinuity, state the conditions in the continuity checklist that are violated. <IMAGE>

Determine the points on the interval (0, 5) at which the following functions f have discontinuities. At each point of discontinuity, state the conditions in the continuity checklist that are violated. <IMAGE>

Determine the points on the interval (0, 5) at which the following functions f have discontinuities. At each point of discontinuity, state the conditions in the continuity checklist that are violated. <IMAGE>

Evaluate f(3) if lim x→3^− f(x)=5,lim x→3^+ f(x)=6, and f is right-continuous at x=3.

What is the domain of f(x)=e^x/x and where is f continuous?

Assume you invest $250 at the end of each year for 10 years at an annual interest rate of $r$. The amount of money in your account after 10 years is given by $A\left(r\right)=\frac{250({(1+r)}^{10}-1)}{r}$. Assume your goal is to have $3500 in your account after 10 years.

b. Use a calculator to estimate the interest rate required to reach your financial goal.

Find an interval containing a solution to the equation $2x=\cos \left(x\right)$. Use a graphing utility to approximate the solution.