Let and for . (i) Obtain in terms of . (ii) Show that for every…

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Let

x=\ln t

and

y=e^{2t}

for

t>0

. (i) Obtain

\dfrac{d^{2}y}{dx^{2}}

in terms of

t

. (ii) Show that

\dfrac{d^{2}y}{dx^{2}}>0

for every

t>0

.

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