[SOLVED] Find the limit (if it exists). If

> Use a graphing utility to graph the function. Use the graph to determine any x-values at which the function is not continuous. f(x) = [[x]] - x

> Discuss the continuity of the composite function h(x) = f(g(x)). f(x) = sin x g(x) = x2

> Discuss the continuity of the composite function h(x) = f(g(x)). f(x) = tan x g(x) = x / 2

> Find an equation of the line that is tangent to the graph of f and parallel to the given line. Function: f(x) = 1 / √x - 1 Line: x + 2y + 7 = 0

> Discuss the continuity of the composite function h(x) = f(g(x)). f(x) = 1 / √x g(x) = x - 1

> Discuss the continuity of the composite function h(x) = f(g(x)). f(x) = 1 / x - 6 g(x) = x2 + 5

> Discuss the continuity of the composite function h(x) = f(g(x)). f(x) = 5x + 1 g(x) = x3

> Discuss the continuity of the composite function h(x) = f(g(x)). f(x) = x2 g(x) = x – 1

> Find the constant a, or the constants a and b, such that the function is continuous on the entire real number line.

> Find an equation of the line that is tangent to the graph of f and parallel to the given line. Function: f(x) = 1 / √x Line: x + 2y - 6 = 0

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = tan πx / 2

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = csc 2x

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = 2│x - 3│ / x - 3

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = │x + 7│ / x + 7

> Find an equation of the line that is tangent to the graph of f and parallel to the given line. Function: f(x) = x3 + 2 Line: 3x - y - 4 = 0

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = x + 2 / x2 – x - 6

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = x + 2 / x2 – 3x - 10

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = x / x2 – 4

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = x / x2 – x

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = sin x – 8x

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = 3x – cos x

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = 1 / x2 + 1

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = 1 / 4 – x2

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = 4 / x - 6

> Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = 6 / x

> Find an equation of the line that is tangent to the graph of f and parallel to the given line. Function: f(x) = x3 Line: 3x - y + 1 = 0

> Discuss the continuity of the function on the closed interval. Function: g(x) = 1 / x2 - 4 Interval: [-1, 2]

> Discuss the continuity of the function on the closed interval. Function: / Interval: [-1, 4]

> Discuss the continuity of the function on the closed interval. Function: f(t) = 3 - √9 – t2 Interval: [-3, 3]

> Discuss the continuity of the function on the closed interval. Function: g(x) = √49 – x2 Interval: [-7, 7]

> Discuss the continuity of the function.

> Discuss the continuity of the function. f(x) = x2 - 1/x + 1

> Discuss the continuity of the function. f(x) = 1/x2 - 4

> Find the limit (if it exists). If it does not exist, explain why.

> Find an equation of the line that is tangent to the graph of f and parallel to the given line. Function: f(x) = 2x2 Line: 4x + y + 3 = 0

> Find the limit (if it exists). If it does not exist, explain why.

> Find an equation of the line that is tangent to the graph of f and parallel to the given line. Function: f(x) = -1/4 x2 Line: x + y = 0

> Find the limit (if it exists). If it does not exist, explain why.

> find the limit (if it exists). If it does not exist, explain why.

> Use the graph to determine each limit, and discuss the continuity of the function. a. / b. / c. /

> (a) Find an equation of the tangent line to the graph of f at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. f(x) = x - 1

> Use the graph to determine each limit, and discuss the continuity of the function. a. / b. / c. /

> In your own words, explain the Intermediate Value Theorem.

> Determine whether / exists. Explain.

> What is the value of c?

> In your own words, describe what it means for a function to be continuous at a point.

> b. Use your answer to part (a) to derive the approximation cos x ≈ 1 – ½ x2 for x near 0. c. Use your answer to part (b) to approximate cos(0.1). d. Use a calculator to approximate cos(0.1) to four decimal places. Compare the result with part (a). /

> Consider f(x) = sec x – 1 / x2 a. Find the domain of f. b. Use a graphing utility to graph f. Is the domain of f obvious from the graph? If not, explain. c. Use the graph of f to approximate / d. Confirm your answer to part (c) analytically.

> (a) Find an equation of the tangent line to the graph of f at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. f(x) = x + 4

> Let

> Prove the second part of Theorem 1.9.

> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If f(x) = g(x) for all real numbers other than x = 0 and

> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

> When using a graphing utility to generate a table to approximate a student concluded that the limit was 0.01745 rather than 1. Determine the probable cause of the error.

> Find a function f to show that the converse of Exercise 112 (b) is not true. [Hint: Find a function f such that / │ f(x)│ = │L│ but / f(x) does not exist.]

> (a) Find an equation of the tangent line to the graph of f at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. f(x) = √x -

> Use the graph shown in the figure. Identify or sketch each of the quantities on the figure. a. f(1) and f(4) b. f(4) â f(1) c. 4 â 1 d. /

> a. Prove that if /│f(x)│ = 0 then /f(x) =0 b. Prove that if / f(x) = L, then / │ f(x)│ = │L│. [Hint: Use the inequality ││f(x)│ − │L││ ≤ │ f(x) − L│.]

> Prove that if / = 0 and │g(x)│≤ M for a fixed number M and all x ≠ c, then / [ f(x)g(x)] = 0.

> Prove that if / = 0 then /

> Prove Property 1 of Theorem 1.2.

> Prove Property 3 of Theorem 1.1. (You may use Property 3 of Theorem 1.2.)

> Prove Property 1 of Theorem 1.1.

> Prove that if / exists and / does not exist, then /does not exist.

> Find two functions f and g such that / and / do not exist, but does exist.

Question: Find the limit (if it exists). If