Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
The first one is of order 5, so it has either 1, 3 or 5 real roots (unless any coefficent was complex). Proof complete :)
The other one, if it has a solution, it must be in [-1;1]. Because it only gives positive results the solution is further restricted to [0;1]. Because the cosine function is continuous and strictly decreasing on this interval, the difference of x and it's cosine will shrink up to some point within the interval where it gets to 0 (the solution) and then flips sign (the cosine gets less than the number), further decreasing until the end of the interval.
The other one, if it has a solution, it must be in [-1;1]. Because it only gives positive results the solution is further restricted to [0;1]. Because the cosine function is continuous and strictly decreasing on this interval, the difference of x and it's cosine will shrink up to some point within the interval where it gets to 0 (the solution) and then flips sign (the cosine gets less than the number), further decreasing until the end of the interval.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
