solutionQ9A - Solutions to Quiz 9A...

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Unformatted text preview: Solutions to Quiz 9A www.math.ufl.edu/˜harringt November 26, 2006 1. (1 pt.) Let g (x) = ln(x8 ), find g (x). Solution: g (x) = ln(x8 ) = 8 ∗ ln(x), so g (x) = 8 ∗ 1 x = 8 x 2. (2 pts.) Let f (x) = xx , find f (x). Solution: Let y = f (x) so y = xx . Thus, y ln(y ) 1 dy y dx 1 dy y dx dy dx dy dx = xx = ln(xx ) = x ln(x) 1 = x + ln x x = 1 + ln x = y (1 + ln x) = xx (1 + ln x) So, f (x) = xx (1 + ln x). 3. (1 pt.) Let h(x) = e3 + 2e + ln(5), find h (x). Solution: Since h(x) is just a number, then the derivative is zero. Hence, h (x) = 0. (If you don’t believe that it’s just a number, type it in your calculator!) 4. (1 pt.) True or False. If f (x) = ln(bx ) where b > 0 and b = 1, then f (x) = ln(b). Solution: This is a true statement. Let’s see why: f (x) = ln(bx ) = x ∗ ln(b). Recall that ln(b) is just a number. (We need, b > 0 so that ln(b) is defined.) Thus, f (x) = ln(b). 1 ...
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