Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. y = 2 x + 3 ,   y = 0 ,   x = 0 ,   x = 1 {“version”:”1.1″,”math”:”y=\sqrt{2x+3},\ y=0, \ x=0, \ x=1″} Note:  V = ∫ a b π ( R ( x ) ) 2 d x {“version”:”1.1″,”math”:”$$V=\int_a^b\pi(R(x))^2dx$$”}

a n = 1 + 11 n n {“version”:”1.1″,”math”:”a_n = \frac{1+\sqrt{11n}}{n}”}Determine whether the nonincreasing sequence converges or diverges.

Express the integrand as a sum of partial fractions and evaluate the integral. ∫ 7 x − 9 x 2 − 4 x − 21 d x {“version”:”1.1″,”math”:”\int \frac{7x-9}{x^2-4x-21}dx”}

Find the length of the curve. y = 2 x 3 / 2 ,  from  x = 0  to  x = 5 4 {“version”:”1.1″,”math”:”y=2x^{3/2}, \text{ from } x=0 \text{ to } x=\frac{5}{4}”} Note:  L = ∫ a b ( 1 + ( f ′ ( x ) ) 2 ) d x {“version”:”1.1″,”math”:”L=\int_a^b\left(\sqrt{1+(f'(x))^2}\right)dx”}

Please select “True.” (Question omitted.)

Consider the following approximations for the first derivative: (forward difference formula}) (center difference formula) In class, we learned how the truncation and round-off errors for the center difference formula are proportional to h2 and , respectively [assume machine precision is ]. Minimizing the total error, yields an optimal step size . (a) The truncation and round-off errors for the forward difference formula are proportional to h and , respectively. Minimize the total error to find the optimal step size . Hint: < . [10 points] (b) Evaluate the derivative of at x = 1 using the two formulae with their respective optimal step sizes. Which formula is more more accurate? The true derivative is e. [5 points]

The medical model proposes that it is useful to think of abnormal behaviour as a disease. … However, in recent decades, … some critics are troubled because medical diagnoses of abnormal behaviour pin potentially derogatory labels on people (Hinshaw, 2007).(Source: Psychology. Themes and variations. By Wayne Weiten. 10th edition. 2017. Boston, USA. Cengage Learning.Chapter 14 Psychological disorders. Page 492)What are some of the derogatory labels we give to people who behave abnormally?

What would be the most logical arrangement of the following sentences in a paragraph? Choose the correct option.Recent findings also indicate the potential for the use of traditional remedies for the management of diabetes.Studies show that culturally appropriate treatment can assist with the treatment of mental illness.Plants used by the traditional healers in South Africa to treat mental illnesses (epilepsy, depression, age-related dementia and debilitative mental disorders) are shown to have profound neurochemical effects.(Source: Health Intelligence magazine. Mar/Apr 2015, Issue 32. Article titled “Which doctor?” by B. Hirschmann. Page 39)

What is the main idea in the Extract below?  As always, across the world, the most vulnerable have borne the brunt of this latest health crisis. COVID-19 has simply further highlighted and exacerbated existing inequalities. Redressing health disparities cannot be effectively achieved during times of crisis, but instead requires longer-term sustained action: through policies and interventions that tackle key social determinants. (Taken from an article titled “A stronger and more united Africa?” Written by Marisa Casale, in Africa in Fact, page 17. Issue 55, October-December 2020.)

A close study of the use of noun phrases (highlighted) in the Extract below provides a quick summary of what the focus of the description is. What is the focus? When we think of OR [Oliver Tambo] what comes to mind is the most gentle soul, with the most tiger-like spirit; the kindest heart, with the fiercest determination; the most compassionate nature, with the strongest moral compass; the warmest, sweetest personality, with an unflinching dedication to honesty; the most loving, peaceful temperament, with the sharpest sense of conscience; the most beautiful smile, with a resolve to accept only absolute integrity; the most noble, patient, calm presence, with the most tenacious fervor for bold, uncompromising action; and the most brilliant intellect, with the most earnest, sincere appreciation for the simplest contribution. (Taken from the book titled Oliver Tambo remembered, edited by Z Pallo Jordan. Memoir by Nadine Hack and Jerry Dunfey, titled “Irresistable, inspirational and deeply loved”. Section with the heading: Friends and neighbours in the UK. Page 3. Johannesburg: Macmillan.)