Explanation Given information: A definite integral of the form ∫ a b f ( x ) d x is approximated by midpoint rule as shown in the figure below, Explanation: Theinput for calculating definite integral ∫ a b f ( x ) d x using midpoint rule, the format on ti- 84 calculator is given below: sum ( seq ( f ( x ) ) , X , a + Δ x 2 , b − Δ x 2 , Δ x ) ⋅ Δ x After implementing midpoint rule, store the result in variable M . By comparing the format of midpoint rule with the input given in above figure, f ( x ) = 1 25 − x 2 , a + Δ x 2 = 3.1 , b − Δ x 2 = 4.9 , Δ x = 0.2 Substitute the value of Δ x = 0.2 in a + Δ x 2 = 3.1 , ⇒ a + 0.2 2 = 3.1 ⇒ a = 3.1 − 1 ⇒ a = 3 Substitute the value of Δ x = 0

Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version

14th Edition

ISBN: 9780134463230

Author: Larry J. Goldstein, David I Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 9.4, Problem 35E

To determine

f(x), a, b and n using the following figure which gives a definite integral of the form ∫abf(x) dx is approximated by midpoint rule as shown in the figure below,

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.4, Problem 34E

Chapter 9.4, Problem 36E

Students have asked these similar questions

A ladder 25 feet long is leaning against the wall of a building. Initially, the foot of the ladder is 7 feet from the wall. The foot of the ladder begins to slide at a rate of 2 ft/sec, causing the top of the ladder to slide down the wall. The location of the foot of the ladder, its x coordinate, at time t seconds is given by x(t)=7+2t. wall y(1) 25 ft. ladder x(1) ground (a) Find the formula for the location of the top of the ladder, the y coordinate, as a function of time t. The formula for y(t)= √ 25² - (7+2t)² (b) The domain of t values for y(t) ranges from 0 (c) Calculate the average velocity of the top of the ladder on each of these time intervals (correct to three decimal places): . (Put your cursor in the box, click and a palette will come up to help you enter your symbolic answer.) time interval ave velocity [0,2] -0.766 [6,8] -3.225 time interval ave velocity -1.224 -9.798 [2,4] [8,9] (d) Find a time interval [a,9] so that the average velocity of the top of the ladder on this…

Total marks 15 3. (i) Let FRN Rm be a mapping and x = RN is a given point. Which of the following statements are true? Construct counterex- amples for any that are false. (a) If F is continuous at x then F is differentiable at x. (b) If F is differentiable at x then F is continuous at x. If F is differentiable at x then F has all 1st order partial (c) derivatives at x. (d) If all 1st order partial derivatives of F exist and are con- tinuous on RN then F is differentiable at x. [5 Marks] (ii) Let mappings F= (F1, F2) R³ → R² and G=(G1, G2) R² → R² : be defined by F₁ (x1, x2, x3) = x1 + x², G1(1, 2) = 31, F2(x1, x2, x3) = x² + x3, G2(1, 2)=sin(1+ y2). By using the chain rule, calculate the Jacobian matrix of the mapping GoF R3 R², i.e., JGoF(x1, x2, x3). What is JGOF(0, 0, 0)? (iii) [7 Marks] Give reasons why the mapping Go F is differentiable at (0, 0, 0) R³ and determine the derivative matrix D(GF)(0, 0, 0). [3 Marks]

5. (i) Let f R2 R be defined by f(x1, x2) = x² - 4x1x2 + 2x3. Find all local minima of f on R². (ii) [10 Marks] Give an example of a function f: R2 R which is not bounded above and has exactly one critical point, which is a minimum. Justify briefly Total marks 15 your answer. [5 Marks]

Chapter 9 Solutions

Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

f ( x ) , a , b and n using the following figure which gives a definite integral of the form ∫ a b f ( x ) d x is approximated by midpoint rule as shown in the figure below,

Solution Summary: The author explains how a definite integral is approximated by midpoint rule. The format of the ti-84 calculator is given below.

Concept explainers

Videos

f(x), a, b and n using the following figure which gives a definite integral of the form ∫abf(x) dx is approximated by midpoint rule as shown in the figure below,

Want to see the full answer?

Chapter 9 Solutions