Problems for Week 1 - Additional Exercises 1. If f ( x ) = x + cos x, find ...
Problems for Week 1 - Additional Exercises 1. If f ( x ) = x + cos x, find ...
Problems for Week 1 - Additional Exercises 1. If f ( x ) = x + cos x, find ...
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is increasing and concave downward.2⎛ r9. Use the Laws of Logarithms to expand ⎟ ⎞ln ⎜.⎝ 3 s ⎠2 210. Use the Laws of Logarithms to expand ln a ( b + c ) .__________________________________________________________In problems 11 and 12 do the following:Make a rough sketch of the graph of each function. Do not use a calculator. Just usethe graph of y = ln x shown in the figure and, if necessary, the trans<strong>for</strong>mations ofSection <strong>1.</strong>3.1<strong>1.</strong> y = ln | x |12. y = ln ( x + 3 )_______________________________________________________________________________________________________________________________________________________________________________13. Differentiate f and <strong>find</strong> the domain of f if f ( x ) = ln ( ln ( ln ( x )) ) .14. <strong>If</strong> g is the inverse of f ( x ) = 2x + ln x, <strong>find</strong> g′ (2).ln(1 + x)15. Use the definition of the derivative to prove that lim = <strong>1.</strong>x→0 x16. (a) Simplify1⎜ .⎝ eln15⎛ ⎞e (b) Simplify ln ⎟⎠x17. (a) Simplify ln( e sin ) (b) Simplify( x ln x)e + .x18. Make a rough sketch of the graph of the function: y = e − .xDo not use a calculator. Just use the graph of y = e shown inthe figure and, if necessary, the trans<strong>for</strong>mations of Section <strong>1.</strong>3in the Stewart textbook.19. Find the inverse function:2y = (ln x) , x > <strong>1.</strong>
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