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→Review Problems
'''4.''' Using the definition of "limit" given above, find <math>\lim_{x \rightarrow 0} \frac{\sin(x)}{x} \ </math>.
'''4.''' Using the definition of "limit" given above, find <math>\lim_{x \rightarrow 0} \frac{\sin(x)}{x} \ </math>.
'''5.''' Using the limit rules given in question 3 and the definitions of derivative, prove
<math>\frac{d}{dx} (f(x)+g(x)) = f'(x) + g'(x) \ </math>
and <math>\frac{d}{dx} x^n = nx^{n-1} \ </math>
'''6.''' Find the derivative of <math>5+e^x-2ax^3 + \sin(x^2) \ </math>, where <math>a \ </math> is a constant.
'''7.''' Give an antiderivative of <math>\log(x) + 3x^2 \ </math>