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 . 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: < . (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.

What conclusion can be drawn from the extract below? Choose the most suitable option.Preventive treatment was associated with a reduction in TB disease among children who had tuberculin skin test conversion (aHR, 0.23; 95% CI, 0.12 to 0.47). However, most cases of TB disease (78 of 98; 79%) occurred among children who had tuberculin skin test conversion but were not administered preventive treatment.

What can we conclude from the extract below:”To the best of our knowledge, this is the first birth cohort study to prospectively investigate M tuberculosis infection and tuberculosis disease in the first decade of life in an area with a high tuberculosis burden,”

What is another suitable reporting verb for saying as it is used in the extract below? Wilhelm Röntgen was awarded the first Nobel Prize for his investigations into X-rays (Physics). However, he refused to limit the potential uses of X-rays by taking out patents, saying that his discoveries belonged to humanity, and gave away his Nobel Prize money. (Taken from The Science Book, edited by R. Colson, C. Halliman & D. John, 2015. London: Penguin Random House, page 187.)

Most large medical aids use biokineticists to screen for chronic conditions such as hypertension, diabetes and hypercholesterolemia. (Source: www.biokineticsSA.org.za) What does the expression to screen for mean in the above extract?

The paraphrase for the following extract has kept certain words. Why? Choose the correct option. The referencing in the paraphrase is correct, so do not concentrate on this.The original text or extract:Furthermore, study results have shown that the survivors are not a homogeneous group, and that the heterogeneity is indicative of differences in post-traumatic adjustment (Kaminer & Lavie, cited in Stroebe, Stroebe & Hansson, 1993: 334).The paraphrase of the above:In addition, research findings have revealed that survivors do not comprise a homogeneous group; rather, heterogeneity characterises differences in post-traumatic adjustment (Kaminer & Lavie, cited in Stroebe, Stroebe & Hansson, 1993: 334).

South African study finds high risk of TB infection in kids Chris Dall, MA November 6, 2024 Tuberculosis Alissa Eckert, James Archer / CDC A prospective birth cohort study conducted in South Africa found that children who grow up in a setting where tuberculosis (TB) transmission is common have a high risk of TB infection and disease, with up to 10% developing the disease by age 10, researchers reported yesterday in The Lancet Child & Adolescent Health. Although 1.2 million children globally develop TB disease every year, and roughly 200,000 die from it, few studies have investigated the risk of developing TB during childhood, particularly in high-burden countries like South Africa. Approximately 15% to 20% of all TB cases in South Africa, which has one of the highest TB incidence rates in the world, are likely to occur in children. To assess the risk, researchers from the Boston University School of Public Health (BUSPH), the University of Cape Town, and the University of Sao Paulo followed 1,137 women and their 1,143 children who were living near Cape Town from 2012 through 2023 and were enrolled in the Drakenstein Child Health Study, a cohort study of children born in a setting with high TB and HIV burdens. A previous study of this cohort found high rates of tuberculin skin test conversion (presumptive evidence of TB infection) and TB disease in the first 5 years of life. For this study, the researchers extended their work to examine the children through the first 10 years of life. They tested the children for Mycobacterium tuberculosis infection and TB disease using tuberculin skin tests at 6 months and 12 months of age, then annually in children with a negative test.  “To the best of our knowledge, this is the first birth cohort study to prospectively investigate M tuberculosis infection and tuberculosis disease in the first decade of life in an area with a high tuberculosis burden,” the study authors wrote. An urgent health problem Over the follow-up period, the annual risk of tuberculin skin test conversion was 6.6 per 100 person-years, ranging from 4.4 to 9.3, with the greatest annual risk occurring at 1 year (9.3%) and 8 years (8.9%). The cumulative hazard of tuberculin skin test conversion was 36% at age 8 years, and the cumulative hazard of TB disease was 10% at age 10.  “These results are striking and show that children in these communities in South Africa are at extraordinarily high risk,” study co-senior author Leonardo Martinez, PhD, MPH, assistant professor of epidemiology at BUSPH, said in a university press release. “It’s clearly an urgent health problem with both short and long-term impacts on these children and their families.” Among the risk factors associated with tuberculin skin test conversion were household cigarette smoke exposure (adjusted hazard ratio , 1.7; 95% confidence interval , 1.2 to 2.5), households with more than five people (aHR, 1.3; 95% CI, 1.1 to 1.7), and known exposure to an individual with TB (aHR, 1.2; 95% CI, 1.0 to 1.6). These results are striking and show that children in these communities in South Africa are at extraordinarily high risk. Preventive treatment was associated with a reduction in TB disease among children who had tuberculin skin test conversion (aHR, 0.23; 95% CI, 0.12 to 0.47). However, most cases of TB disease (78 of 98; 79%) occurred among children who had tuberculin skin test conversion but were not administered preventive treatment. “This highlights an important challenge in tuberculosis programmes where provision of preventive treatment is of low priority,” the authors write. Martinez and his colleagues say children who develop TB disease are at risk for poor outcomes in young adulthood and later life and that follow-up on this cohort to understand their long-term health trajectories is an important next step. They also call for a multipronged approach to decrease pediatric TB in high-burden settings that combines preventive treatment for children at risk, active case finding, and reduction of community TB transmission. Read the extract below and answer the question: A prospective birth cohort study conducted in South Africa found that children who grow up in a setting where tuberculosis (TB) transmission is common have a high risk of TB infection and disease… What do you understand by birth cohort? Choose the most appropriate option below:

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 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.)

What is missing from the sentence below?For decades the standard way to prevent people who were exposed to tuberculosis (TB) from falling ill with the disease was to offer them a medicine called isoniazid, taken daily for six or more months.

Examine the word drought-resistant in Extract below. This is a compound word containing a noun (drought) and adjective (resistant). How is this compound word functioning in this extract?Figs are very tough and drought-resistant once established, however, fruit production will decline if not provided with adequate moisture.