2. For the following data, assume the data follows the rule f (x)=1/(Ax+B). Using the transformation...
a-f Differentiate the following by using the product rule: w 9x² – 2)(3x + 1) (c) x² (4x+6) (e) (2 - x)(1+x)(x+21 (b) (3x + 10)(6x2 - 7x) (d) (ax - b)(cx2) (f) (x2 + 3)x-1 co Given AR = 60 - 3Q, plot the average-revenue curve, and then find the MRC
1. Use Cramer's rule to solve this system. X + 4z = 2 2x + y -z= 1 X +z=-1 on 910 2. Given the data points (0,), (1,3), (2,5) use the equation y=f(x) = mx +b to find the least square solution for best line fit. a. Evaluate the equation using the data points to obtain four linear equations. b. Write the system in 10a in a matrix form Ax=b. durants bhonebnih 516 10 boer word c. Write the...
Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomials P1(x), P2(x), Pa(x). b) Evaluate f(2.5) by using Pa(x). c) Obtain a bound for the errors E1(x), E2(x), Es(x) Exercise 7: Consider f(x)- In(x) use the following formula to answer the given questions '(x) +16-30f+16f,- 12h a) Derive the numerical differentiation formula using Taylor Series and find the truncation error b) Approximate f'(1.2) with h-0.05...
using discrete structures 3. Consider the function F(x, y, z) for x, y, z z 0 defined as follows: a. F(x, y, 0)-y+1 b. F(x, 0, 1)-x c, F(x, 0, 2) = 0 d. F(x, 0, z+ 3)-1 e. F(x, y, z)-F(x, F(x, y-1, z), z-1) Using Induction, prove the following a. F(x, y, 1)-x +y b, F(x, y, 2) = xy c. F(x, y, 3)-xy 3. Consider the function F(x, y, z) for x, y, z z 0 defined...
f(x) = 2.10 Consider the following algorithm (known as Horner's rule) to evaluate -ax': poly = 0; for( i=n; i>=0; i--) poly = x * poly + ai a. Show how the steps are performed by this algorithm for x = 3, f(x) = 4x + 8x + x + 2. b. Explain why this algorithm works. c. What is the running time of this algorithm?
This Question: 1 pt For y = f(x)=2x-1, x= 3, and Ax=2 find a) Ay for the given x and Ax values, b) dy = f'(x)dx, c) dy for the given x and Ax values a) Ay = || (Round to four decimal places as needed b) dy = f'(x)dx= ( ) ox Bound to two decimal places as seeded
2. For the difference cquation, X2+] = ax, + b = f(x,), where 0 <a < 1 and b> 0, use the solution given in (1.12) to find the following limit: lim ->XX7. Show that this limit is also a fixed point of the difference cquation, that is, it is a solution x of t = f(x) (see Figure 1.2).
To find the instantaneous rate of change at x=3 Using the definition f(x +Ax) - f(x) Slope T - lim Ar-0 To find the instantaneous rate of change at x 3
Solve the equation Ax b by using the LU factorization given for A. Also solve Ax b by ordinary row reduction. 3 -5 1 0 0 3 5 4 4 A = 19 -3 1 3 -1 1 0 0 - 4 1 6 2 -6 2 3 1 0 1 58 - Let Ly b and Ux y. Solve for x and y. y X = Row reduce the augmented matrix [A b] and use it to find x...
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives of the collowing: f)-(3442) fool(3x+2) (-5x + x + 1) - 2 1 =(-15x 10x" + (-2x = 2) =>15x410x5 - 2x = = 3x -3x- 27 (X)(3+0)-(3x+2)(1) x² g'=(x) =F12x15x4_2 = -5x6 xb * please check my work, if wrong, please write out correct solation! Chain Rule: When functions are composed, to take the derivative involves both the outside function and the inside...