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In a curve y = t2 + 2t and x = t3, find the slope \(\rm dy\over dx\) at t = 51. \(\rm \frac{4}{5}\)2. \(\rm \frac{4}{3}\)3. \(\rm \frac{12}{5}\)4. \(\rm \frac{4}{25}\) |
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Answer» Correct Answer - Option 4 : \(\rm \frac{4}{25}\) Concept: Parametric Form: If f(x) and g(x) are the functions in x, then \(\rm df(x)\over dg(x)\) = \(\rm \frac{df(x)\over dx}{dg(x)\over dx}\)
Calculation: Given y = t2 + 2t \(\rm {dy\over dt}\) = 2t + 2 Also x = t3 \(\rm dx\over dt\) = 3t2 Now \(\rm dy\over dx\) = \(\rm \frac{dy\over dt}{dx\over dt}\) \(\rm dy\over dx\) = \(\rm \frac{2t +2}{3t^2}\) At t = 5, \(\rm {dy\over dx}\) = \(\rm \frac{2(5) +2}{3(5)^2}\) = \(\rm \frac{12}{75}\) = \(\rm \frac{4}{25}\) |
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