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Let $\displaystyle f(x) = \sqrt{x^{2}+10x+49}$ .

(a) Find the tangent line approximation, $L(x)$ , at $x = 0$ .

$L(x)$ =

(b) Use the tangent line to approximate the value of $f(0.25)$

$f(0.25) \approx$ (Use at least 2 decimal places)

(c) Find the error function, $E(x)$ , for the given approximation.

$E(x)$ =

(d) Calculate the error in the tangent line approximation at $x = 0.25$ . In other words, find $E(0.25)$ .

$E(0.25)$ = (Round to at least 3 decimal places)