1) You are using the Bisection Method to approximate a root of f(x) = x3 -72x - 220 within the interval [9,10]. What is the new interval after one iteration?  a) [8,9] b) [9,9.5] c) [9.5,10] d) [9.25,9.75] 2) Given the data points: (1,1), (-2,1), (3,2)  What is the slope m at the least-square regression line y= mx+b? a) 23/38 b) 15/38 c) 19/23 d) 38/23 3) What is the derivative used in the Newton-Raphson method for f(x) = x2 + 8x +15? a) x+8 b) 2x+8 c) x2+15 d) 2x 4) Which of the following best describes the Newton-Raphson method? a) It uses fixed-point iteration b) It simplifies the equation algebraically c) It always gives exact answers d) It approximates roots using a tangent line and iteration 5) In the bisection method, what condition must be satisfied to begin the method? a) f(x1) = f(x2) b) f(x1) ⋅ f(x2)>0 c) f(x1) =0 d) f(x1) ⋅ f(x2)<0 6) Which method uses linear interpolation to estimate the root? a) Newton-Raphson Method b) Bisection Method c) False-Position Method d) Incremental Search 7) In the graphical method, where is the root located? a) Where the graph intersects the y-axis b) Where the function equals zero c) Where the function has maximum slope d) Where the function is undefined 8) What is the purpose of the least-squares regression method? a) To eliminate all errors b) To solve equations graphically c) To fit a line that minimizes the sum of the squared errors d) To find roots of non-linear equations 9) ​Given the least-squares regression equation y = mx+b, what does m represent? a) Y-intercept b) Mean of y c) Error margin d) Slope 10) If y = xn , then the derivative dy/dx is: a) n ⋅ xn+1 b) xn-1 c) n ⋅ xn-1 d) n ⋅ xn 11) In the bisection method, if f(0.5) = 0.107 and f(10 = -0.632, what can we conclude? a) Root lies between 0.5 and 1 b) Root lies before 0 c) No root in the interval d) Root lies exactly at 0.5 12) ​How does the False-Position method calculate the next approximation? a) Midpoint between left and right b) Newton-Raphson formula c) Linear interpolation between xL and xR d) Graphical estimation 13) GIVEN: (-1,0), (0,2), (1,4), (k,5) with m= 1.7, b= 1.9 What is the value of k that satisfies the regression line? a) 1 b) 2 c) 3 d) 0 14) In curve fitting, what does the equation y= mx + b represent? a) Derivative of a function b) Regression line c) Equation for interpolation d) Second-order polynomial 15) GIVEN: f(x) = e-x - x  According to the presentation, what is the approximate root of f(x) = e-1 -x, using the bisection method? a) 0.3156 b) 0.5671 c) 1.2310 d) 0.8042

Numerical Methods

bởi
In
Nhúng

Bảng xếp hạng

Phong cách trực quan

Tùy chọn

Chuyển đổi mẫu

Bạn có muốn khôi phục tự động lưu: không?