your copy of the test is p 16) The ONLY DIFFERENCE between the Newton-Raphson method and the Secant method is that a) Secant requires you to know the first derivative b) Newton-Raphson needs the first derivative c) Secant requires the second derivative d) Newton-Raphson is an iterative procedure Identify these Numerical Methods from their descriptions b) Gauss-Jordan Elimination d) Centered difference approximations e) Bisection 17) The fourth order Runge-Kutta method uses weights of 1/6, 2/6 1) Solve simultaneous linear equations 2) Find a zero of any continuous function 3) Use least squares to find a first order polynomial with best fit 4) Match x/y-values with a high order polynomial 5) Calculate numerical values for derivatives of a function 2/6 and 1/6 to combine values of f(x, y) evaluated at four points. What is fx, y) equal to a) a pseudo random variable (PRV) b) The first derivative in an ordinary differential equation c) The definite integral of a transcendental function the SUM of the functions f(x) and f(y) d) used for approximating b) Identify these 5 Numerical Methods from their descriptions 18) Difference quotients or finite divided difference formu a) b) c) Newton Raphson method Simpson's rule Quadratic Spline interpolation es Second Derivatives d) Any order Derivatives e) Taylor Series Approximations 19) Numerical integration is better than algebraic integration 6) Use an initial point and the slope field f (x.y) to predict subsequent values of a function f(x) Use weighted sums to calculate the area under a curve Use the value of a function and its derivatives at one value of x to approximate the function at a different value of x. a) It is easier to program b) It is inherently more accurate c) It is faster to calculate d) None of the above is true 7) 8) 20) Normally, when you run a Javascript program, it is embed 9) Use the first derivative to find zeroes of a function 10) Use second degree polynomials to find intermediate values for in a file with the extension a) JS b) PROG c) HTM d) 21) Which technique can find coefficients for a quadratic spli 11) What's the best way to fix a program that isn't working? a) Throw it away and rewrite it b) Try randomly changing instructions until you get a d) all of the abo Gaussian Elimination b) a) 22) What is the weakness of Euler's method for solving an The weighting functions are not optimal c) Try it with different data d) Have the computer tell you the results of each step b) It can not be used with sinusoidal curves c) The derivative at the start of an interval does not ap 12) Which method starts with an initial guess close to the root? the whole interval d) They only work with continuous functions 23) Which statement is NOT a valid way to start a repeating 24) Which of the following methods will not solve an ODE. 25) Suppose you find an interval [xo, Xi] over which a funct 13) The true percent relative error is given by the formula abs( ((true value) - (computer result)) / (true value)) Why is this formula hardly ever used? a) We don't want to divide by zero b) We usually don't know the true value a) if b) for c) do d) while un There is truncation error in this formula d) changes sign between fxo) and f(xi). The Bisection Met estimates the root to be at: Actually we did use this formula most of the time 14) Which of the following will ALWAYS calculate the zero of a 26) The goal of linear regression is to create a unique linev function in a closed interval [a,b] as long as f(a)*f(b)0? a) bisection method c) True Value Method b) Newton's method d) Secant method Passes through all data points b) ) Best fits a given set of data points. Always passes through the first and last data points d) Maximizes the sum of the squares of the residuals 15) The Taylor Series uses an infinite number of terms involving derivatives and factorials. Why can this method be used? a) We only use a finite number terms with values like EXP(O) 27) What is a Maclaurin series? a) A Trigonometric series centered at zero b) A root finding algorithm c) A Taylor series centered at zero d) A differential equation. to approximate an unknown like EXP(x) and they We have powerful computers that can calculate an infinite number of values We can calculate factorials pretty easily Actually, it is useless and only of theoretical interest b) c) d)