Mathematics

Problem

Let

y=e^{\sqrt{1+2x^{2}}}

. a. (i) Derive an exact expression for

\dfrac{dy}{dx}

in its simplest form. b. (ii) Evaluate

\dfrac{dy}{dx}

x=0

. c. (iii) Using your result from part (i), find the limit

\lim_{x\to0}\frac{e^{\sqrt{1+2x^{2}}}-e}{x},

and write the answer in terms of

e