
Match each of the following functions, f, with p: its (truncated) Taylor polynomial approx- imation about a = 0. (d) f(x) = V4+. (a) f(x) = {x?; (b) f(x) = e-62; (@) f(x) = cos(2x); (1) p(x) = 1 – 62 +18x2 – 3624 – 32470. (i) P(x) = 2 + - 64 x2 + 5127 (ii) P(x) = 1 – 2x2 + xy - 1 10. (iv) p(x) = 1 +2° +2° +
21. Find the derivative of each of the following functions by applying the product rule a. f(x) = (x2 + 1][2x2 + 3x + 4) b. f(x) = x2 cos x c. f(x) = e* sin x 22. Find Find the derivative of each of the following functions by applying the quotient rule a. f(x) = 22+1 f(x) = (2x + 1] / [x - 3] b. f(x) = x+2x+1 3x + 1 c. f(x) = sing 23. Find the...
For the function f(x) = e 2x, which of the following polynomials is the 2nd degree Taylor polynomial for f(2') at the point I = 0? 1) P(x) = 1-2+x2 2) P2 (3)=1-23 +22 3) P3(x) = 1 - 2.c + 2x2 4) P4(x) = 1 + 2x + 2x2 O Polynomial in 3) Polynomial in 1) O Polynomial in 2) O Polynomial in 4)
Find the Taylor polynomial of order 3 centered at 0. f(x) = com 6-X pg(x) = - * x4 x2 36 + + x3 216 x2 216 + х 36 + + P3(x) = 5 P3(x) = 1296 x3 1296 x4 1296 x2 + 6 36 x3 216 x2 216 P3(x) = х 1 6 + x3 1296 36 Find the quadratic approximation of fat x = 0. f(x) = sin In(2x + 1) P2(x) = 2x + 2x2 p2(x)...
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
7. Give the formula of avoiding roundoff error to solve each of the fol- lowing problem and compute the numerical values. All the results are approximated to 4 digits with rounding arithmetic. (1). Find the roots of the quadratic equation 123 1 2+ 1 0 4 6 (Hint: first observe b and 62 - 4ac) -5+ b2 - 4ac c/a (Answer:21 22 = ; 21 = 92.24, 22 2a I 1 10-3) 5.420 x 9 (2). Compute In (50 –...
Use substitution of trigonometric functions but please
give answers in terms of x and it should be simplified
1 x2 - x 3. Find indefinite integrals of these functions: (a) V1 + 4x2; (b) 4 - 22; (c) : () (22 - 1)3/2
Prob.II. Differentiate the following functions, and simplify. 1. f(x) 2x-3 x+4 2. f(x) = x²(x - 2)* 3. f(x) = In (x V1 - x2) 4. f(x) = x2e-* 5. Find dy/dx = y' for the equation x2 + y2 = 25 and find y" (check H.W)
(1) Find the Taylor series about 0 for the following functions: (a) ce (b) sin(x), (c) V1 + x (d) cos(x)
9. Find the relative and absolute max and min of the following functions a. f(x)=x'+x b, f(x) = Vx+4 64 c. f(x) = x3-2x2 + 5 d. f(x)- x2+4
9. Find the relative and absolute max and min of the following functions a. f(x)=x'+x b, f(x) = Vx+4 64 c. f(x) = x3-2x2 + 5 d. f(x)- x2+4