MATH SOLVE

3 months ago

Q:
# What is the slope of the tangent line to the parametric curve x = t^2 + 2t, y = t^2 + 1 at t = 1? (4 points) 1/2 1/4 4 2

Accepted Solution

A:

ANSWER[tex] \frac{1}{2} [/tex]EXPLANATIONThe given parametric curve has equation:[tex]x = {t}^{2} + 2t[/tex]and[tex]y = {t}^{2} + 1[/tex]Let us differentiate each equationtion with respect to t.[tex] \frac{dx}{dt} = 2t + 2[/tex]and[tex] \frac{dy}{dt} = 2t[/tex]The slope function is given by:[tex] \frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} } [/tex]This implies that:[tex] \frac{dy}{dx} = \frac{2t}{2t + 2} [/tex]At t=1,[tex] \frac{dy}{dx} = \frac{2(1)}{2(1)+ 2} [/tex][tex] \frac{dy}{dx} = \frac{2}{4} [/tex][tex] \frac{dy}{dx} = \frac{1}{2} [/tex]The correct choice is A.