TRUE OR FALSE. The parametric curve x = f(t), y = g(t) has a vertical tangent line at a point where t = 2 if f'(2) = 0.

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A: I am attaching image so that you understand each and every step.

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Q: (æ² + 1)² x²ez² 2(x2 + 1) + C x²ez? 2(z² + 1) -ze +C O A Ов 1 2(x2 + 1) cea 2 2(2² + 1) - 2" +C…

A: The given integral is: I=∫x3ex2(x2+1)2dx=∫x2ex2(x2+1)2x dx Substitute x2=u⇒2xdx=du⇒xdx=du2 So,…