{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

practice-quiz2-sol

# practice-quiz2-sol - AMS 151(Fall 2009 Joe Mitchell Applied...

This preview shows pages 1–2. Sign up to view the full content.

AMS 151 (Fall, 2009) Joe Mitchell Applied Calculus I Practice Problems for Quiz # 2 – Solution Notes 1. Solve for x : 4 · 2 2 x - 1 - 3 · 5 x = 0. 4 · 2 2 x - 1 = 3 · 5 x ln 4 + ln 2 2 x - 1 = ln 3 + ln 5 x ln 4 + (2 x - 1) ln 2 = ln 3 + x ln 5 (2 ln 2 - ln 5) x = ln 3 - ln 4 - ln 2 x = ln 3 - ln 4 - ln 2 2 ln 2 - ln 5 = ln(3 / 8) ln(4 / 5) 2. Determine which function has a larger value as x → ∞ : (a). f ( x ) = 5 · x 2 - 57 x or g ( x ) = 0 . 002 · (1 . 001) x g ( x ) grows faster, since is is exponential (proportional to 1 . 001 x ), while f ( x ) is polynomial (grows like x 2 ). (b). f ( x ) = log 4 x or g ( x ) = 3 · log 2 x 3 f ( x ) grows faster, since it grows like log 4 x , while g ( x ) grows like log 2 x (a lower power of logarithm). 3. Find the inverse function of y = g ( t ) = 3 e t +4 - 2. 2 + y 3 = e t +4 ln( 2 + y 3 ) = t + 4 t = ln( 2 + y 3 ) - 4 Thus, g - 1 ( y ) = ln( 2+ y 3 ) - 4. 4. Let y = h ( x ) = 2 3 - e - x 2 . (a). Is h increasing or decreasing? x 2 is increasing, so - x 2 is decreasing, so e - x 2 is decreasing, so - e - x 2 is increasing, so 2 3 - e - x 2 is decreasing. (b). Find a formula for h - 1 ( u ).

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

practice-quiz2-sol - AMS 151(Fall 2009 Joe Mitchell Applied...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online