lecture19hout

# lecture19hout - MATH 006 Calculus and Linear Algebra...

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MATH 006 Calculus and Linear Algebra (Lecture 19) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 14

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Outline 1 Continuous Compound Interest and the Constant e 2 Derivative of e x 3 Derivative of ln x 4 Derivatives of Other Exponential and Logarithmic Functions Albert Ku (HKUST) MATH 006 2 / 14
Continuous Compound Interest and the Constant e The Constant e Deﬁnition The number e is deﬁned by e = lim n →∞ ± 1 + 1 n ² n = lim s 0 (1 + s ) 1 / s 2 . 7182818284590 ..... If a principal P is borrowed at an annual rate r , then after t years, the borrower will owe the lender an amount A given by A = P ³ 1 + r n ´ nt . Now we let n go to inﬁnity, we ﬁnd that lim n →∞ P ³ 1 + r n ´ nt = P lim n →∞ ³ 1 + r n ´ ( n / r ) rt = P [lim s 0 (1 + s ) 1 / s ] rt = Pe rt . The above formula is called the continuous compound interest formula . Albert Ku (HKUST) MATH 006 3 / 14

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Continuous Compound Interest and the Constant e Example If \$100 is invested at 6%, what amount will be in the account after 2
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## This note was uploaded on 12/28/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

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lecture19hout - MATH 006 Calculus and Linear Algebra...

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