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Next: Exam 2 Up: Calculus I Reviews and Previous: Exam 1

Review for 2nd Exam

  1. Exercises 1-52, page 159.
  2. Find $ g^{\prime\prime\prime}(-\pi/8)$ if $ g(t)=\csc 2 t$ .
  3. Find an equation of the tangent line to the curve at the given point.
    1. $\displaystyle y=\frac{x}{x^{2}-2}, \quad (2, 1)
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    2. $\displaystyle y=\tan x , \quad (\pi/3, \sqrt{3})
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    3. $\displaystyle y=x \sqrt{1+x^{2}} , \quad (1, \sqrt{2})
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  4. Find $ y^{\prime}$ if $ x \tan y = y-1$ .
  5. Find $ y^{\prime\prime}$ if $ x^{6}+y^{6}=1$ .
  6. Find the equation of the tangent line for the equation $ y^3-xy=-6$ at $ (7,2)$ .
  7. Find the local linearization of $ f(x)=\ln(1+x)$ near $ x=0$ .
  8. Find the local linearization of $ f(x)=\sqrt[3]{1+3x}$ near $ x=0$ .
  9. Exercises 2, 4 and 6 on page 158.
  10. Find the limit.
    1. $\displaystyle \lim_{x \rightarrow 0} \frac{\sec x}{1 - \sin x}
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    2. $\displaystyle \lim_{t \rightarrow 0} \frac{t^{3}}{\tan^{3} 2 t}
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    3. $\displaystyle \lim_{x \rightarrow 0^{+}} x \ln x
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lagcc 2004-08-09