1 Functions (1.3)
... The division is little bit more involved since we can’t divide by zero and therefore the domain of ( f / g )( x ) = f ( x ) / g ( x ) must also exclude all zeros of g ( x ) , i.e. ...
... The division is little bit more involved since we can’t divide by zero and therefore the domain of ( f / g )( x ) = f ( x ) / g ( x ) must also exclude all zeros of g ( x ) , i.e. ...
Exercises for Unit I V (The basic number systems of mathematics)
... The so – called sequence of Fibonacci numbers is given recursively by the formulas F0 = F1 = 1 and Fn = F n – 1 + F n – 2 for n > 1. Find a function H as in the recursive definition theorem which can be used to define the sequence of Fibonacci numbers. [ Hint : The cases n = 1 and n > 1 must be hand ...
... The so – called sequence of Fibonacci numbers is given recursively by the formulas F0 = F1 = 1 and Fn = F n – 1 + F n – 2 for n > 1. Find a function H as in the recursive definition theorem which can be used to define the sequence of Fibonacci numbers. [ Hint : The cases n = 1 and n > 1 must be hand ...
Math 111 – Calculus I
... (d) Is the function symmetric with respect to the y-axis? Is the function symmetric with respect to the origin? Are there other symmetries you can determine? (e) Using your graphing calculator, sketch the graph in an “appropriate window”. ...
... (d) Is the function symmetric with respect to the y-axis? Is the function symmetric with respect to the origin? Are there other symmetries you can determine? (e) Using your graphing calculator, sketch the graph in an “appropriate window”. ...
6.9 Modeling with polynomial functions
... • Now solve for a! 2=6a so, a=1/3 • Answer: f(x)=1/3(x+2)(x-1)(x-3) ...
... • Now solve for a! 2=6a so, a=1/3 • Answer: f(x)=1/3(x+2)(x-1)(x-3) ...
Math/CS 466/666 Lecture 06 The Quadratic Equation Made Difficult
... More complicated formulae for solving cubic and quartic equations exist. The appropriate algebraic transformation to avoid loss of precision when using these formulae for numerical calculation are also more complicated. Moreover, it was proved by Abel in 1824 that no general formula exists for the s ...
... More complicated formulae for solving cubic and quartic equations exist. The appropriate algebraic transformation to avoid loss of precision when using these formulae for numerical calculation are also more complicated. Moreover, it was proved by Abel in 1824 that no general formula exists for the s ...
![[2014 question paper]](http://s1.studyres.com/store/data/008843331_1-92d678c1b1e5e59d0d7cea147d7fb096-300x300.png)
[2014 question paper]
... B1. Find the area of the region in the XY plane consisting of all points in the set {(x, y)|x2 + y 2 ≤ 144 and sin(2x + 3y) ≤ 0}. B2. Let x be a real number such that x2014 − x2004 and x2009 − x2004 are both integers. Show that x is an integer. (Hint: it may be useful to first prove that x is ration ...
... B1. Find the area of the region in the XY plane consisting of all points in the set {(x, y)|x2 + y 2 ≤ 144 and sin(2x + 3y) ≤ 0}. B2. Let x be a real number such that x2014 − x2004 and x2009 − x2004 are both integers. Show that x is an integer. (Hint: it may be useful to first prove that x is ration ...
ADMISSIONS EXERCISE MSc in Mathematical and Computational
... down before successfully producing three widgets? (iii) For a fixed value of r, calculate the expected value of αY , for α > 0. (iv) Using Markov’s inequality or otherwise, show that for any q ∈ [p, 1], there exists a constant C such that P (Y > x) ≤ Cq x . ...
... down before successfully producing three widgets? (iii) For a fixed value of r, calculate the expected value of αY , for α > 0. (iv) Using Markov’s inequality or otherwise, show that for any q ∈ [p, 1], there exists a constant C such that P (Y > x) ≤ Cq x . ...
REAL NUMBERS - University of British Columbia Department
... interval our number is located. We then take that small interval and cut it up into 10 very small equal pieces ...
... interval our number is located. We then take that small interval and cut it up into 10 very small equal pieces ...
1.2 – Transforming Functions Transformations describe a set of
... 1.2 – Transforming Functions Transformations describe a set of processes that starts with an original function and then multiplies or adds to this function to create another function. Depending whether this is done inside or outside the function determines whether this effects the input (horizontal) ...
... 1.2 – Transforming Functions Transformations describe a set of processes that starts with an original function and then multiplies or adds to this function to create another function. Depending whether this is done inside or outside the function determines whether this effects the input (horizontal) ...