exponential_slides

# exponential_slides - Question The natural logarithm is a...

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The natural logarithm is a one-to-one function. A) true B) False Hint: think of the graph of ln(x). Question

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Horizontal Line Test. If f is one-to-one, then each horizontal line meets the graph of f in at most one point. ln(x) is one-to-one
ln(x) is one-to-one ln(x) is invertible Define the exponential function e x to be the inverse of the natural logarithm ln(x) =ln(x) =e x

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=ln(x) =e x Note: The inverse function f -1 undoes whatever f does… So we get: ln(e x ) = x e ln(x) = x
The expression e ln(3a)+ln(6b) is equivalent to: A) 3a+6b B) (3a)(6b) Question

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Find all the solution of the equation ln(x 2 -3e 2 )=2. A) ± 2e B) I don’t know Question
e x e y = e x+y Properties of the exponential function e x /e y = e x-y (e x ) r = e rx r rational

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A) 1 B) 2 C) 4 D) 5 The exponential function e x is the inverse of the logarithm ln(x). Identify the graph of e x. Question
…the graph of f -1 is obtained by flipping the graph of f about the line y=x

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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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