Reverse Polish Notation. We remarked at the beginning of this section that mathematicians usually put the operation symbol between the two objects (operands) to which the operation applies. There is, however, an alternative notation in which the operationsymbol comes after the two operands. This notation is called reverse Polish notation(RPN for short) or postfix notation. For example, in RPN, instead of writing 2 C 3, wewrite 2 3 C.Consider the RPN expression 2; 3; 4; C;. There are two operation symbols, andeach operates on the two operands to its left. What do the C and operate on? TheC sign immediately follows 3; 4, so it means to add those two numbers. This reducesthe problem to 2; 7;. Now the operates on the 2 and the 7 to give 14. Overall, theexpression 2; 3; 4; C; in standard notation is 2 .3 C 4/.On the other hand, the RPN expression 2; 3; C; 4; stands for .2 C 3/ 4, whichevaluates to 20.Evaluate each of the following.a. 1; 1; 1; 1; C; C; C.b. 1; 2; 3; 4;; C; C.c. 1; 2; C; 3; 4;; C.d. 1; 2; C; 3; 4; C;.e. 1; 2; C; 3; C; 4;.40.23. RPN
Math 103—Week 2 Notes—1.52.2 1.5: Exponential Rules: If a > 0 and b > 0… a • a = a x+y x a xy y = a a (a ) = (a ) = axy a • b = (ab)x x a a x x = ( ) b b Exponential Growth/ Decay: kx y = y 0 exponential growth if k > 0 exponential decay if k < 0 *y is a constant 0 y = Pe continuously compounded interest model P is initial monetary investment r is interest rate (decimal form) t is time (in units consistent with r) 1.6: Onetoone function: when each range value (y) has one distinct domain value (x) Passes the horizontal line test Inverse Functions: 1 Notation: f (x) f (b) =a if f(a) =b The domain of f is the range of f and the range of f is the domain of f **To find and/or graph an inverse function, switch x and y values in the original function Ex: 1 Find the inverse of y = x + 1 2 1 x = y + 1 2 2x = y + 2 y = 2x – 2 Logarithmic Functions: y = log a is the inverse of y = a (a > 0, a ≠ 1) y = ln x is the inverse of y = e x log 10= logx log e = lnx ln e = 1 Algebraic Properties: lnbx = lnb + lnx Product rule b ln = lnb – ln x Quotient rule x 1 ln = lnx Reciprocal rule x lnx = rlnx Power rule Inverse Properties: alog = x (a > 0, a ≠ 1, x > 0) a x log a = x (a > 0, a ≠ 1, x > 0) e
