What isthe thirddegree Taylor polynomial for g(x)= Vx centered at a = 1? A.1-*-1)+(x-1° -(x-1)° 2 4 8 1 1 1 (x+1)––(x+1) (x+1)² +(x+1)° 4 2 8 1 C.1+(x- 1)- 2 1 (x – 1) + 8 1 (x-1)° 16 1 D.1--(x+1)+-(x+1) 8 1 (x+1)° 16 2 O A O B OC
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- Suppose g is a function which has continuous derivatives, and that g(8) = -2, g(8) = 3. g"(8) = -4, g"(8) = 4. %3D (a) What is the Taylor polynomial of degree 2 for g near 8? P:(z) = (b) What is the Taylor polynomial of degree 3 for g near 8? Pa(z) = (c) Use the two polynomials that you found in parts (a) and (b) to approximate g(8.1). With Pa, g(8.1) = With Ps, g(8.1) =Suppose g is a function which has continuous derivatives, and that g(8) = -1, g'(8) = 2, g"(8) = 5, g"(8) = -5. (a) What is the Taylor polynomial of degree 2 for g near 8? P2(x) = (b) What is the Taylor polynomial of degree 3 for g near 8? P3(x) = (c) Use the two polynomials that you found in parts (a) and (b) to approximate g(7.9). With P2, 9(7.9) = With P3, g(7.9) -Suppose g is a function which has continuous derivatives, and that g(6) = -2, g' (6) = 5, g" (6) = 1, g" (6) = 5. (a) What is the Taylor polynomial of degree 2 for g near 6? P2(x) = (b) What is the Taylor polynomial of degree 3 for g near 6? P3(x) = (c) Use the two polynomials that you found in parts (a) and (b) to approximate g(6.1). With P2, g(6.1) With P3, g(6.1) 2
- Suppose g is a function which has continuous derivatives, and that g(2) = -2, g (2) = -4, g"(2) = 2, g" (2) = 3. (a) What is the Taylor polynomial of degree 2 for g near 2? P2(x) = (b) What is the Taylor polynomial of degree 3 for g near 2? P3(x) : (c) Use the two polynomials that you found in parts (a) and (b) to approximate g(1.9). With P2, g(1.9) - With P3, g(1.9) -Find the first four of the Taylor the function 1/x about the point a = -1 (Your answers should include the variable x when appropriate) 1/x = ?+?+?+? I got 1/x= -1/0!+ (x+1)/1!+-2(x+1)^2/2!+(6(x+1))/3! However, (x+1)/1! And (6(x+1))/3! Is incorrect. Please help me.if 13 x = 0 (1) (2) (3) X 1+x² (1) ex³ (2) X (3) 1 x ln(1 + x) 6th Taylor polynomial 10th Taylor polynomial 3rd Taylor polynomial
- Express p(x) = 1 + 2x -5x2 as a Taylor polynomial about a= -2.Suppose g is a function which has continuous derivatives, and that g(8) = 3, g'(8) = 3, g"(8) = −2, g""(8) = 1. (a) What is the Taylor polynomial of degree 2 for near 8? P₂(x) = 3 + 3(x − 8) − (x − 8)². (b) What is the Taylor polynomial of degree 3 for Ps(x) = 3 + 3(x− 8) – (x−8)² = 2 + (x-8)³ 6 g near 8? (c) Use the two polynomials that you found in parts (a) and (b) to approximate g(8.1). With P2, g(8.1) ≈ With P3, g(8.1) ≈Find y' by (a) applying the Product Rule and (b) multiplying the factors to produce a sum of simpler terms to differentiate. y = (8x² + 5) (x+3+ -1) a. Apply the Product Rule. Let u = (8x² + 5) and v= = (ax² + 5) and v= (x+3+ -] +5) 0 + (x+³+ -) 0 +3 d dx (uv) = (8x² +
- Express p (x) = 1 + 2x - 5x2 as a Taylor polynomial about a=l.Find the coefficient on x^10 in each of the generating functions below. (h) (1-x^14)/(1-x)What is the sixth-order Taylor polynomial for f(x) = /1+2x² about Xo = 0? x6 (A) 1 + x² + 8 16 x4 (B) 1 – x² - 2 2 x4 X' (C) 1 + x² – + (D) 1 + x2 .4 + 2 2 + 2 3x2 1+ 2 9x4 + 16 (E) 27x6