Question 1
Find all the roots of the equation sin x = x
2.
◦ 0, 0.876726
◦ 0.876833
◦ 0, 0.876833
◦ 0.876726
◦ ± 0.876726
Question 2
Give the iteration formula for finding the roots of the equation sin x - x
2 = 0 using Newton's Method.
◦ x
n+1 = x
n -
![](data:image/png;base64, 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)
◦ x
n+1 = x
n +
![](data:image/png;base64, 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)
◦ x
n+1 = x
n -
![](data:image/png;base64, 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)
◦ x
n+1 = x
n -
![](data:image/png;base64, /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAMCAgMCAgMDAwMEAwMEBQgFBQQEBQoHBwYIDAoMDAsKCwsNDhIQDQ4RDgsLEBYQERMUFRUVDA8XGBYUGBIUFRT/2wBDAQMEBAUEBQkFBQkUDQsNFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBT/wAARCAAyAFQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD9U6K+ff2n/ihf+BtT0OxtfHln4LiuLS5uPLhubKPVb2ZSgijtYb2CSG5BJYGFXilYsm1wM15P4a+POk2S6dZad8XdP0nVLz4iSaZqcTRaPBc3aT24Y/aI0hAE0bAIsi871CyGUgg5KpFu39fEo/m/+AErRV2+/wCEXJ/gvxPtW5uobKB57iaOCFBlpJWCqo9yeBUtfKfhzx7qeq+P9P8Ah74j8aDxLNovxDeznnu1tIb2e3j0o39ktxHDGiD/AEgZVljTcbYY5BrR8F/GLW0+JbaNqPi+517wndT3Vz4U1mG2son8TSxrtl0vztiQFonEpQr5TShVIcrFKz7NNWb2auvSyf367W6eaQLVN9nb8Wvu03/ydvpiWVIInlldY40UszucBQOpJ7CiKVJ4kkjdZI3AZXQ5DA9CD3FeS+Df2j9O8Zav4Os/+ES8TaPaeLIJn0zU9SitPs7zRRvJLbOIrh5EkVYpDkp5bBTtduM3PgLcSp4K1+xtGjuLbSvEOr6fp0bMEjSGK7kWOHKqdqp/qxwSAnekrNX8r/p/w3foVZ2v5pfem/0189D1GiuI8Gav8SL7Vmj8WeFPC2iaZ5RK3GjeJ7nUZjJkYUxSafbgLjPzb8jA4OePIte+LWr6D8ZptLl8cyN8Ob3VIrGXxB9ltMaLqq5Y6R53l7AkwMQ3yqzqzNF5nmSR+W+qXf8A4b+v82rz0cui/r+vv2Tt9KV5bF4m8f6J8X9H0XVz4f1Xw1rsN5JBDpdpPDe6UIAjB5pHmdbiNt6oWWOHa8kYw2azbT9peylutNW68EeK9OsrrXz4Zn1C4jsmhsb7zhDGkvl3TOVd2ULJErqNwDFSCBf8H/D74iaH48vdc1jxn4X1mxvZm86KPwtcQXq243eVbx3B1F0REyP+WJ3HcSNzFqULSSmno/8AL/Jpr5MqS5bxe66fNr9GvX8PVaKKKCQorwnxT8Ev2ZfA9xp8HiPwD8J/D8+ozC3sotU0bTLZrqUnASMOgLsfRcmm2/wW/Zju/GM3hKDwH8JZvFcEXnS6FHo+mNfRx4B3tAE3heRyRjkUk09v6tuD03PYvEvhu18U6elrdNLE0U8V1BcQMFlgmjcOjqSCMgjkEEMCVYFSQb1/bSXljc28V1NYyyxsiXVuEMkJIwHUOrLuHUblIyOQRxXzjdeA/wBlyef7DoXw/wDhL4l1r+0odIOmaZpWlyyx3Mhb5JQqEx7USWRgRnbE+ASMHf8A+FK/sxn+0f8Aig/hN/xLb2PTb3/iT6Z/ot3IVWO3l+T5JWLoAjYYlhgcilo9O/8AwP8AgfgPVO/X/h/+D+Js6J+zlZ6D4c8CaVB408TyS+Db6W90/UpvsLXEokilieGb/RRGybJnGQiv0O/IzXpfhrw7ZeEtCtNJ05HS0tVKp5jl3YkkszMeWZmJYk9SSa89/wCGTvgh/wBEb+H/AP4S9j/8arnvCPwA+BHit9Ztv+FLfD+01LR75rC+s28N2DtE4VXRuIvuvG8cikgHDjIBzVxWnLHZf8MTa2p7tRXlX/DJ3wQ/6I38P/8Awl7H/wCNV5r8Wfg18NvhpGNYtv2a/hvrfhK0MR1S9XTbGG+iRnCs9va/ZGWcIGyQ0sTHBChjjMj8zvov2brVfCepaHN448U3TXniOLxRHqUv9n/abS8S4S4Aj22gjKGRASro/GQCBjHsNeEf8KV/ZjP9o/8AFB/Cb/iW3sem3v8AxJ9M/wBFu5Cqx28vyfJKxdAEbDEsMDkV0X/DJ3wQ/wCiN/D/AP8ACXsf/jVKCSgox2/4C/SwNe85Pd3v97b/ABbPVaKqaTpNjoGlWWmaZZW+nabZQpbWtnaRLFDBEihUjRFACqqgAKAAAABRVAeba14I8V2fxbv/ABDplh4f8R+H9c0+003ULTW7yW2msUgkmbdBtt5lmV/OJMbeX8yg7znA4WP9n7xbeTaJoeop4Zk8P+HfEVz4ksNcilmGpXckjTssEsIiVYv+PjZJMszmREIKLvOPo6iocVL4tf6uvue343Qrb+f/AAz+9f8AA11PlXQPhR40+HPiPwJ4l1tdN0zw34au4rFtHsNYn1dYbZ7e5thcm7ubaOdUja5jAhZnSOMyPvHNdxr/AMIvF138ZbT4m6evh+HVbOcaZ/Zcs8ohvNK2uBPJMIdyXiGaYoAjoEZ48/vDIPcqK0u9/wCtd/1+TttaxbRrvb8Nv0+5d3f47sPjhqcXh3/hL7f40xazoug/EJPDupLMulGzl06a+SENcyxwK0bokhZJEaNSFXcr8sfe/hXazXvi74ieI1Xbper6rClg/I8+O3tYoXlwQBhpEkCsCQyopHBFek0VEFy01GWrXX5Jfo/vfqVJtzlJaX6eV27fil8jhNI+DHh/RPFI8QW+oeLJL8SvN5N34x1e5s9zZyPsst00G35jhdm1eMAYGMD4lab8TNW8Z2J0bw54U1zwlY+VdRW+q+JrrTppbxW3LJKkenzqyxkKyLvxuG85ITb61RWkW42t0C+/meF638I/GN58YrL4m2SeHrfWLOZdNbSZLiXyLzS9rgTSTiHct4hmmKfIyBGaPP7wyL5fYfHDU4vDv/CX2/xpi1nRdB+ISeHdSWZdKNnLp018kIa5ljgVo3RJCySI0akKu5X5Y/YlFZpNTjK+i6fNP8bP/wACfoKbcotLRvr8mv1X/gK9QoooqgCiiigAooooAKKKKACiiigAooooAKKKKAP/2Q==)
◦ x
n+1 = x
n +