
a.
To describe the test for Divergence.
a.

Answer to Problem 5RCC
If the limit of
Explanation of Solution
Given information:
test for Divergence.
If the limit of
Therefore,
b.
To describe the integral test.
b.

Answer to Problem 5RCC
Integral test is defined as the test in which a non-negative function which is defined on the unbounded interval
Explanation of Solution
Given information:
To describe the integral test.
Let,
And it converges to a real number if and only if the improper integral
Hence,
Integral test is defined as the test in which a non-negative function which is defined on the unbounded interval
c.
To describe the comparison test.
c.

Answer to Problem 5RCC
Comparison test is defined as the test in which one series or integral whose convergence properties is to be determined is compared with the series or integral whose convergence properties is known.
Explanation of Solution
Given information:
the comparison test.
Comparison test is defined as the test in which one series or integral whose convergence properties is to be determined is compared with the series or integral whose convergence properties is known.
For, series, the comparison test is defined by,
If the infinite series
d.
To describe the limit comparison test.
d.

Answer to Problem 5RCC
Limit comparison test is defined as the test in which the two series (
Explanation of Solution
Given information:
The limit comparison test.
Limit comparison test is defined as the test in which the two series (
e.
To describe the alternating series test.
e.

Answer to Problem 5RCC
Alternating series test is defined as the test in which an alternating series
Explanation of Solution
Given information:
The alternating series test.
Consider, an alternating series,
Where,
Alternating series test is defined as the test in which an alternating series
f.
To describe the ratio test.
f.

Answer to Problem 5RCC
The ratio test use the limit of form
The ratiotest states that if
Explanation of Solution
Given information:
the ratio test.
The ratio test use the limit of form
The ratiotest states that if
Chapter 8 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Explain the conditions under which the Radius of Convergence of the Power Series is a "finite positive real number" r>0arrow_forwardThis means that when the Radius of Convergence of the Power Series is a "finite positive real number" r>0, then every point x of the Power Series on (-r, r) will absolutely converge (x ∈ (-r, r)). Moreover, every point x on the Power Series (-∞, -r)U(r, +∞) will diverge (|x| >r). Please explain it.arrow_forwardExplain the conditions under which Radious of Convergence of Power Series is infinite. Explain what will happen?arrow_forward
- Explain the conditions under Radius of Convergence which of Power Series is 0arrow_forwardExplain the key points and reasons for 12.8.2 (1) and 12.8.2 (2)arrow_forwardQ1: A slider in a machine moves along a fixed straight rod. Its distance x cm along the rod is given below for various values of the time. Find the velocity and acceleration of the slider when t = 0.3 seconds. t(seconds) x(cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 30.13 31.62 32.87 33.64 33.95 33.81 33.24 Q2: Using the Runge-Kutta method of fourth order, solve for y atr = 1.2, From dy_2xy +et = dx x²+xc* Take h=0.2. given x = 1, y = 0 Q3:Approximate the solution of the following equation using finite difference method. ly -(1-y= y = x), y(1) = 2 and y(3) = −1 On the interval (1≤x≤3).(taking h=0.5).arrow_forward
- Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?arrow_forward1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist, state that fact. и (a) f'(-5) (b) f'(-3) (c) f'(0) (d) f'(5) 2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5) = 4. - 3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2) and f'(2).arrow_forwardDoes the series converge or divergearrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





