1. Limits and Continuity

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.

What does it mean for a function to be continuous on an interval?

Complete the following steps for each function.

c. State the interval(s) of continuity.

f(x)={2x if x<1

x^2+3x if x≥1; a=1

Complete the following steps for each function.

c. State the interval(s) of continuity.

f(x)={x^3+4x+1 if x≤0

2x^3 if x>0; a=0

Determine the interval(s) on which the following functions are continuous. At which finite endpoints of the intervals of continuity is f continuous from the left or continuous from the right? 

f(x)=√25−x^2

Determine the interval(s) on which the following functions are continuous. At which finite endpoints of the intervals of continuity is f continuous from the left or continuous from the right? 

f(x)=√x^2−3x+2

Determine the interval(s) on which the following functions are continuous. At which finite endpoints of the intervals of continuity is f continuous from the left or continuous from the right? 

f(t)=(t^2−1)^3/2

Determine the interval(s) on which the following functions are continuous. At which finite endpoints of the intervals of continuity is f continuous from the left or continuous from the right? 

f(x)=(2x−3)^2/3