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**Unformatted text preview: **Recall that if f is one-to-one… Note: lim x !" e x = + " lim x !#" e x = y=e x B) -Find the value of value of the limit A) + C) 0 Question lim x ! 2 + e 3/(2 " x ) ! ! B) -Find the value of value of the limit A) + C) 0 Question lim x ! 2 e 3/(2 " x ) 2 ! ! A) B) e x C) ln(x) The exponential function e x is the inverse of the logarithm function f(x)=ln(x). The derivative of ln(x) is f’(x)=1/x. Find the derivative of e x =f-1 (x). Hint: d dx f ! 1 ( x ) = 1 f '( f ! 1 ( x )) 1 1/ x = x Question (e x )’=e x • Chain rule: (e f(x) )’=e f(x) f’(x) • Example: (e tan(x) )’=e tan(x) sec 2 (x) The derivative of e x is e x : B) ln(x) A) e x C) 1 Question ! e x dx = ! e x dx = e x 3 ! e x dx = e 3 " e = e 3 " 1. Substitution rule: e f ( x ) ! f '( x ) dx = e f ( x ) + C...

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- Fall '09
- FAMIGLIETTI,C
- Calculus, Derivative, lim, Inverse function, exponential function ex