- For the following exercises, estimate the functional values and the limits from the graph of the function f provided in Figure 14.
- For the following functions, find the equation of the tangent line to the curve at the given point x on the curve.
- For the following exercises, use technology to evaluate the limit. Evaluate the limit by hand. At what value(s) of x is the function
- For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined,
- For the following exercises, evaluate the limits using algebraic techniques.
- For the following exercises, evaluate the limits algebraically.
- For the following exercises, determine why the function f is discontinuous at a given point a on the graph. State which condition fails.
- For the following exercises, determine why the function f is discontinuous at a given point a on the graph. State which condition fails.
- For the following exercises, evaluate the limits algebraically.
- For the following exercises, use the definition of derivative to calculate the derivative of each function.f(x) = 5
- For the following exercises, draw the graph of a function from the functional values and limits provided.
- For the following exercises, assume two die are rolled. What is the probability of rolling a pair?
- For the following exercises, determine why the function f is discontinuous at a given point a on the graph. State which condition fails.
- For the following exercises, evaluate the limits using algebraic techniques.
- For the following exercises, use the definition of a derivative to find the derivative of the given function at x = a.f(x) = 2x2 + 9x
- For the following exercises, use the definition of derivative to calculate the derivative of each function.f(x) = 5π
- For the following exercises, evaluate the limits using algebraic techniques.
- For the following exercises, draw the graph of a function from the functional values and limits provided.
- For the following exercises, draw the graph of a function from the functional values and limits provided.
- For the following exercises, evaluate the limits algebraically.
- For the following exercises, evaluate the limits using algebraic techniques.
- For the following exercises, evaluate the limits algebraically.
- For the following exercises, with the aid of a graphing utility, explain why the function is not differentiable everywhere on its domain. Specify the
- For the following exercises, with the aid of a graphing utility, explain why the function is not differentiable everywhere on its domain. Specify the
- For the following exercises, find the average rate of change between the two points. (−2, 0) and (−4, 5)
- For the following exercises, evaluate the limits using algebraic techniques.
- For the following exercises, evaluate the limits algebraically.
- For the following exercises, find the average rate of change between the two points. (4, −3) and (−2, −1)
- For the following exercises, use numerical evidence to determine whether the limit exists at x = a. If not, describe the behavior of the graph of the
- For the following exercises, evaluate the limits algebraically.
- For the following exercises, explain the notation in words when the height of a projectile in feet, s, is a function of time t in seconds after
- For the following exercises, find the average rate of change between the two points. (0, 5) and (6, 5)
- For the following exercises, use numerical evidence to determine whether the limit exists at x = a. If not, describe the behavior of the graph of the
- For the following exercises, evaluate the limits algebraically.
- For the following exercises, explain the notation in words when the height of a projectile in feet, s, is a function of time t in seconds after
- For the following exercises, find the average rate of change between the two points.(7, −2) and (7, 10)
- For the following exercises, use a graphing calculator to determine the limit to 5 decimal places as x approaches 0. f(x) = (1 + x)1/x
- For the following exercises, explain the notation in words when the height of a projectile in feet, s, is a function of time t in seconds after
- For the following exercises, use numerical evidence to determine whether the limit exists at x = a. If not, describe the behavior of the graph of the
- For the following exercises, evaluate the limits algebraically.
- For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined,
- For the following polynomial functions, find the derivatives. f(x) = x3 + 1
- For the following exercises, use a graphing calculator to determine the limit to 5 decimal places as x approaches 0. g (x) = (1 + x)2/x
- For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined,
- For the following exercises, evaluate the limits algebraically.
- For the following polynomial functions, find the derivatives. f(x) = −3x2 − 7x + 6
- For the following exercises, use a graphing calculator to determine the limit to 5 decimal places as x approaches 0.h(x) = (1 + x)3/x
- For the following exercises, evaluate the limits algebraically.
- For the following exercises, use technology to evaluate the limit.
- For the following polynomial functions, find the derivatives.f(x) = 7x2
- For the following exercises, use a graphing calculator to determine the limit to 5 decimal places as x approaches 0.i(x) = (1 + x)4/x
- For the following exercises, evaluate the limits algebraically.
- For the following exercises, use technology to evaluate the limit.
- For the following exercises, use a graphing calculator to determine the limit to 5 decimal places as x approaches 0.j(x) = (1 + x)5/x
- For the following exercises, use a graphing calculator to determine the limit to 5 decimal places as x approaches 0.Based on the pattern you observed
- For the following polynomial functions, find the derivatives.f(x) = 3x3 + 2x2 + x − 26
- For the following exercises, use technology to evaluate the limit.
- For the following exercises, use a graphing utility to find graphical evidence to determine the left- and right-hand limits of the function given as
- For the following exercises, determine where the given function f(x) is continuous. Where it is not continuous, state which conditions fail, and
- For the following exercises, determine where the given function f(x) is continuous. Where it is not continuous, state which conditions fail, and
- For the following exercises, evaluate the limits algebraically.
- For the following functions, find the equation of the tangent line to the curve at the given point x on the curve. f(x) = 2x2 − 3x x = 3
- For the following exercises, determine where the given function f(x) is continuous. Where it is not continuous, state which conditions fail, and
- For the following exercises, evaluate the limits algebraically.
- For the following functions, find the equation of the tangent line to the curve at the given point x on the curve. f(x) = x3 + 1 x = 2
- For the following exercises, use a graphing utility to find graphical evidence to determine the left- and right-hand limits of the function given as
- For the following exercises, evaluate the limits algebraically.
- For the following exercises, consider the function whose graph appears in Figure 3.Find the average rate of change of the function from x = 1 to x =
- <p style="text-align: justify;">For the following exercises, determine where the given function f(x) is continuous. Where it is not
- For the following exercises, consider the function whose graph appears in Figure 3.Find all values of x at which f′(x) = 0.
- For the following exercise, find k such that the given line is tangent to the graph of the function. f(x) = x2 − kx, y = 4x − 9
- For the following exercises, evaluate the limits algebraically.
- For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and
- For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and
- For the following exercises, consider the function whose graph appears in Figure 3.Find all values of x at which f′(x) does not exist.
- For the following exercise, use the given information to evaluate the limits:
- For the following exercises, consider the function whose graph appears in Figure 3.Find an equation of the tangent line to the graph of f the