Tính tích phân $\int_0^{\pi/2} \sinh(x) dx$.
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cho 0 a pi/2 khẳng định nào sau đây đúng
- Tính tích phân $\int_0^{\pi/2} \arctan(\tan(x)) dx$.
- Tính tích phân $\int_0^{\pi/2} \frac{1}{\sin^2(x) + \cos^2(x)} dx$.
- Tính giới hạn $\lim_{x \to 0^+} \frac{e^x - 1 - x}{x^2}$. Cho hàm số $f(x) = \sin(x) + x$ trên khoảng $(0, \pi/2)$, đạo hàm của $f(x)$ là gì?
- Tính tích phân $\int_0^{\pi/2} \frac{1}{\sin^2(x)} dx$.
- Tính tích phân $\int_0^{\pi/2} \tan(x) dx$.
- Tính tích phân $\int_0^{\pi/2} (\csc(x) - e^x) dx$.
- Tìm giá trị lớn nhất của hàm số $f(x) = x + \sin(x)$ trên khoảng $[0, \pi/2]$.
- Tính giới hạn $\lim_{x \to 0^+} x \cot(x)$. Cho hàm số $f(x) = e^x \cos(x)$ trên khoảng $(0, \pi/2)$, đạo hàm của $f(x)$ là gì?
- Tính giới hạn $\lim_{x \to 0^+} x \sin(1/x^2)$. Cho hàm số $f(x) = a^x$ trên khoảng $(0, \pi/2)$, đạo hàm của $f(x)$ là gì?
- Hàm số $f(x) = \arcsin(\sin(x))$ có liên tục trên $[0, \pi/2]$ không?
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