Use the two$-$point forward$-$difference formula $to$ approximate $f^{\text{'}}(1),$ and find the

approximation error, where $f(x)=lnx,$ for $(a)h=0\mathrm{.}1(b)h=0\mathrm{.}01(c)h=0\mathrm{.}001.$

Use the three$-$point centered$-$difference formula $to$ approximate $f^{\text{'}}(0),$ where $f(x)=e^x,$ for

$(a)h=0\mathrm{.}1(b)h=0\mathrm{.}01(c)h=0\mathrm{.}001.$

Use the two$-$point forward$-$difference formula $to$ approximate $f^{\text{'}}(\frac{}{3}),$ where $f(x)=sinx,$

and find the approximation error. Also, find the bounds implied $by$ the error term and show that

the approximation error lies between them $(a)h=0\mathrm{.}1(b)h=0\mathrm{.}01(c)h=0\mathrm{.}001.$

Carry out the steps $of$ Exercise $3,$ using the three$-$point centered$-$difference formula.

Use the three$-$point centered$-$difference formula for the second derivative $to$ approximate

$f^{\text{'}\text{'}}(1),$ where $f(x)=x^{-1},$ for $(a)h=0\mathrm{.}1(b)h=0\mathrm{.}01(c)h=0\mathrm{.}001.$ Find the approximation

error.

Use the three$-$point centered$-$difference formula for the second derivative $to$ approximate

$f^{\text{'}\text{'}}(0),$ where $f(x)=cosx,$ for $(a)h=0\mathrm{.}1(b)h=0\mathrm{.}01(c)h=0\mathrm{.}001.$ Find the

approximation error.