{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MATH111-200630-PS02-Solutions

# MATH111-200630-PS02-Solutions - Math 111 Problem Set 2...

This preview shows pages 1–3. Sign up to view the full content.

Math 111 Problem Set 2 Solutions Edward Doolittle September 27, 2006 1. (a) 2log 10 3 log 10 90 log 10 3 2 log 10 90 log 10 9 log 10 90 log 10 9 90 log 10 10 1 1. (b) ln e 2 3 2 3 ln e 8 1 8. 2. (a) Exponentiating both sides, e ln 5 x 2 e 7 5 x 2 e 7 5 x e 7 2 x 1 5 e 7 2 My calculator tells me that x 0 4002 to 4 decimal places. (b) Taking the log base 2 of both sides, log 2 2 3 x 4 log 2 10 3 x 4 log 2 2 log 2 10 3 x 4 log 2 10 3 x log 2 10 4 x 1 3 log 2 10 4 Since there is no log 2 button on my calculator I have to use the chain rule for logarithms to evaluate log 2 10 ln 10 ln 2 ; with that, my calculator tells me x 0 2260. 3. (a) Write f x x ln x 1 2 . Then by the chain rule and product rule, f x 1 2 x ln x 1 2 d dx x ln x 1 2 x ln x 1 2 d dx x ln x x d dx ln x 1 2 x ln x 1 2 ln x x 1 x 1 2 x ln x 1 2 ln x 1 (b) Rewrite 2 u in terms of the (natural) exponential function: 2 u e ln2 u e ln2 u . Then by the chain rule, g θ d d θ e ln2 sin θ e ln2 sin θ d d θ ln2 sin θ 2 sin θ ln2 cos θ 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4. (a) Take the logarithm of both sides: ln y ln 2 x 3 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

MATH111-200630-PS02-Solutions - Math 111 Problem Set 2...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online