Day 291: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

Question 1
Definite Integration. Asked once: NDA 1 2019
85 $\displaystyle\int_0^{\pi/2}e^{\sin x}\cos x\,dx$
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Question 2
Differential Equations. Asked once: NDA 1 2019
91 $\dfrac{dy}{dx}+\dfrac{x}{y}=0$
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Question 3 (case study, 3 parts)
Differentiation. Asked once: NDA 1 2023
Consider the following for the next three (03) items that follow: Let $f(x)=\begin{vmatrix}\cos x & x & 1\\2\sin x & x^{2} & 2x\\\tan x & x & 1\end{vmatrix}$ .
76 $f(0)$
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77 $\lim_{x\to0}\dfrac{f(x)}{x}$
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78 $\lim_{x\to0}\dfrac{f(x)}{x^{2}}$
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Question 4
Functions. Asked once: NDA 2 2024
77 $f(x)=[x]^2-30[x]+221=0$
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Question 5
Indefinite Integration. Asked once: NDA 1 2021
86 $\int\frac{dx}{\sec^2(\tan^{-1}x)}$
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Question 1