$10$ cos x $=0$ has two solutions, $t1$ $Tn0$ equation $x^{2}-10$ ±1.3793646. Use Newton's method to approximate the solutions $to$ within $10-5$ with the following values of p,. $\left(a\right)$ $p_{0}=-100$

Consider the IVP $\dfrac {dy} {dt}=\dfrac {y} {t}+1:1\leq t\leq 2,$ $y\left(1\right)=1$ The approximation of $y\left(1.2\right)$ using Taylor's method of order $2$ with $7=$ $0.2$ is Select $Onθ$ a. $2.305$ $b$ $1.420$ $2$ $c.$ $2.620$ d. $1.205$

Use Euler's method to approximate the $1MP$ $y=2y-e^{1}$ $0\leq t\leq 1$ $y\left(0\right)=1$ with $nh=0.1$ Then $y\left(0.2\right)=$ ka a. -1.670517 ob. $0.449482$ $8$ $c.1$ $1.20948$ $d$ d. $0.830517$