Calculus I - Week 03 Notes

Paper Exercises

Exercise 03-01

01

Solve log or exponent equations

Solve for $x$:

• (a) $\ln (x^2-1)=3$
• (b) $\ln x+\ln (x-1)=0$
• (c) $\frac{60}{1+e^{-x}}=4$
• (d) $e^{2t+1}=9e^{1-t}$

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Exercise 03-02

02

Inverse trig practice

Simplify the expression:

• (a) $\sin \left({\cos }^{-1}\left(\frac{y}{5}\right)\right)$
• (b) ${\tan }^{-1}\left(\tan \left(\frac{13\pi }{4}\right)\right)$

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