گاما رو نصب کن!

{{ number }}
اعلان ها
اعلان جدیدی وجود ندارد!
کاربر جدید

جستجو

پربازدیدها: #{{ tag.title }}

جستجوهای پرتکرار

میتونی لایو بذاری!

a) By sketching suitable graphs, show that the equation

$4{x^2} - 1 = \cot x$

has only one root in the interval $0 \lt x \lt \frac{1}{2}\pi $.

b) Verify by calculation that this root lies between 0.6 and 1.

c) Use the iterative formula

${x_{n + 1}} = \frac{1}{2}\sqrt {\left( {1 + \cot {x_n}} \right)} $

to determine the root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.

پاسخ تشریحی :
نمایش پاسخ

a) Make recognisable sketch of a relevant graph over the given range

Sketch the other relevant graph on the same diagram and justify the given statement

b) Consider sign of $4{x^2} - 1 - \cot x$ at $x = 0.6$ and $x = 1$, or equivalent

Complete the argument correctly with correct calculated values

c) Use the iterative formula correctly at least once

Obtain final answer 0.73

Show sufficient iterations to at least 4 d.p. to justify its accuracy to 2 d.p., or show there is a sign change in the interval (0.725, 0.735)

تحلیل ویدئویی تست

تحلیل ویدئویی برای این تست ثبت نشده است!