91Ó°ÊÓ

Some of these can be multiplied out. For a few of these, take the derivative both before and after multiplying out, and compare the two. $$y=x^{2} \sqrt{3-4 x}$$

Evaluate each limit. $$\lim _{x \rightarrow 1} \frac{x^{3}-x^{2}+2 x-2}{x-1}$$

Find the derivative of each function. Check some by calculator. $$y=\left(a+\frac{b}{x}\right)^{3}$$

Limits Involving Zero or Infinity $$\lim _{x \rightarrow 0}\left(4 x^{2}-5 x-8\right)$$

Find the derivative of each function. Check some by calculator. $$y=\sqrt{1-3 x^{2}}$$

The velocity of a moving point is given by the first derivative of the displacement, and the acceleration is given by the second derivative of the displacement. Find the velocity and acceleration at \(t=1.55 \mathrm{s}\), of a point whose displacement is given by $$s=4.55 t^{3}+2.85 t^{2}+5.22 \quad \mathrm{cm}$$ where \(t\) is the elapsed time, in seconds.

Some of these can be multiplied out. For a few of these, take the derivative both before and after multiplying out, and compare the two. $$y=\sqrt{x}\left(3 x^{2}+2 x-3\right)$$

Find \(d y / d x\). (Treat \(a\) and \(r\) as constants.) $$5 x-2 y=7$$

Find the derivative of each function. Verify some of your results by calculator. As usual, the letters \(a, b, c, \ldots\) represent constants. Power Function with Negative Exponent. $$y=\frac{1}{x}$$

Find the slope of the tangent or the rate of change at the given value of \(x\) $$y=\frac{1}{x^{2}} \text { at } x=1$$