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Hogar Banco de preguntas Matemáticas Cálculo Archive 2025 January 12

Calculus Questions from Jan 12,2025

Browse the Calculus Q&A Archive for Jan 12,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Siano e . È vero che per Scegli un alternativa: è un infinitesimo di ordine 2 rispetto a è un infinitesimo di ordine superiore rispetto a è un infinitesimo di ordine 6 rispetto a Derivar: a. b. c. d. 3. Sand is being dropped at the rate of onto a conical pile. If the height of the pile is always twice the base radius, at what rate is the height increasing when the pile is 8 m high? Determine the volume generated by revolving the area between and the x-axis from to about the y-axis with the washer method. Calcule chacune des limites suivantes 55. Prove that 56. Prove that 57. If verify that 58. Express , into partial fractions. Assuming that , obtain an expression for , give your answer in the form of hence, find the value of the coefficients as far as the term in inclusive. 59. Expand as a series of descending power of x as far as the third term, use expansion to find value of by substitution 60. Find the coefficient of the term involving in the expansion of 61. Find the middle term(s) of the following expression 62. If the constant term in the expansion of is 405 ,. Find the value of . 63. Obtain the first four terms of the expansion in ascending power of , hence find the value of correct to four decimal places. 64. Prove that if x is very small that its cube and high power can be neglected by taking . Prove that is approximately to 65. Show that , if and 66. When a polynomial is divided by and has a remainder 2,8 and 2 respectively. Evaluate the value of and 67. Find the value of and in the following system of equations 68. Use binomial expansion to evaluate each of the following (a) (b) 69. Prove that 70. Show that 71. Prove that 72. In the binomial expansion of , where is a positive integer, the coefficient of is times the sum of the coefficients of and . Find the value of and determine these three coefficient 73. Write the first four terms of the expansion of in ascending powers of , hence deduce that Find the first five partial sums of the given series and determine whether the series appears to be convergent or divergent. If it is convergent, find its approximate sum. Ine tourth partial sum is I (Type an integer or decimal rounded to four decimal places as needed.) The fifth partial sum is . (Type an integer or decimal rounded to four decimal places as needed.) The series appears to convergent To what value does this series converge? A. B. C. D. E. The series diverges. \begin{tabular}{l} Find the first five partial sums of the given series and determine whether the series appears to be \\ convergent or divergent. If it is convergent, find its approximate sum. \\ The first partial sum is \( \mathrm{S}_{1}=0.5 \). \\ (Type an integer or decimal rounded to four decimal places as needed.) \\ The second partial sum is \( \mathrm{S}_{2}=0.75 \). \\ (Type an integer or decimal rounded to four decimal places as needed.) \\ The third partial sum is \( \mathrm{S}_{3}=0.9000 \). \\ (Type an integer or decimal rounded to four decimal places as needed.) \\ The fourth partial sum is \( \mathrm{S}_{4}=\square \). \\ (Type an integer or decimal rounded to four decimal places as needed.) \\ \( (n+1)(\mathrm{n}+2) \) \\ \hline\end{tabular} Find the first five partial sums of the given series and determine whether the series appears to be convergent or divergent. If it is convergent, find its approximate sum. The first partial sum is . (Type an integer or decimal rounded to four decimal places as needed.) The second partial sum is . (Type an integer or decimal rounded to four decimal places as needed.)
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