所屬科目：研究所、轉學考(插大)-微積分
A. \( f(x) = \sqrt{4 - 3x^2} \)
B. \( y = 1 + \sin x \)
A. \( \lim_{x\to 1^{-}}f(x) \)
B. \( \lim_{x\to 1^{+}}f(x) \)
C. \( \lim_{x\to 1}f(x) \)
D. \( \lim_{x\to 5}f(x) \)
E. \( f(S) \)
A. \( \lim_{x\to 0}\left(\frac{3x^3 - 2x}{3x^2 + x - 2} -x\right) \)
B. \( \lim_{x\to 1}\frac{\sin(x - 1)}{x^2 + x - 2} \)
A. \( y = \sin x + 10\tan x \)
B. \( \sqrt{x} +\sqrt{y} = 1 \)
A. \( \int x^{2} \ln |x| \, dx \)
B. \( \int_{3}^{6} x e^{4x^2 + 1} dx \)
6. (10%) Find the local extrema of \( f(x) = x^{2}e^{-x} \).
7. (10%) Find the volume of the solid that is bounded by the elliptic paraboloid \( x^{2} + 2y^{2} + z = 16 \), the planes \( x = 2 \), \( y = 2 \), and the three coordinate planes.
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