csat-suneung 2024 Q24_calculus

csat-suneung · South-Korea · csat__math 3 marks Parametric differentiation
For the curve represented parametrically by $$x = \ln(t^3 + 1), \quad y = \sin\pi t$$ where $t > 0$, find the value of $\frac{dy}{dx}$ at $t = 1$. [3 points]
(1) $-\frac{1}{3}\pi$
(2) $-\frac{2}{3}\pi$
(3) $-\pi$
(4) $-\frac{4}{3}\pi$
(5) $-\frac{5}{3}\pi$ 
For the curve represented parametrically by
$$x = \ln(t^3 + 1), \quad y = \sin\pi t$$
where $t > 0$, find the value of $\frac{dy}{dx}$ at $t = 1$. [3 points]\\
(1) $-\frac{1}{3}\pi$\\
(2) $-\frac{2}{3}\pi$\\
(3) $-\pi$\\
(4) $-\frac{4}{3}\pi$\\
(5) $-\frac{5}{3}\pi$
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q23_calculus Q23_geometry Q24 Q24_calculus Q24_geometry Q25 Q25_calculus Q25_geometry Q26 Q26_calculus Q26_geometry Q27 Q27_calculus Q27_geometry Q28 Q28_calculus Q28_geometry Q29 Q29_geometry Q30 Q30_geometry