The value of (9.1)3/2 can be approximated using an appropriate local linear approximation of f(x) =...
3. (8 points) Find an appropriate local linear approximation for the function cos(x) and estimate the value of cos 31°.
24.9 and 25.1. Find the local linear approximation of the function f(x) = V14 + x at Xo = 11, and use it to approximate (a) S(x) = /14+x2 (b)/24.9 - (c) 25.1 - For parts (b) and (c), you should enter your answer as a fraction. If you enter a decimal, make sure that it is correct to at least six decimal places.
7. Find the linear approximation of f(x,y)=-x’ +2y’ at (3,-1) and use this approximation to estimate f(3.1.-1.04). S (3,-1) = (3.-1) = ,(3,-1) = L(x, y)= L(3.1, -1.04) =
Question 6 (2 marks) Not yet answered Find the linear approximation of f(x) = el-* at x = 1 Use the linear approximation to approximate the value of 0.1 and compare it to its exact value. Explain why you can use the linear approximation to estimate eº-1 with high accuracy but not e-4 Marked out of 6.00 (4 marks) Flag question B 32 U X x2 lll E E 23T
3. Cosine Approximation Write a function m-file to calculate the approximated cosine function which can be evaluated by the following infinite series - equation (2): 1. x² x4 26 (-1)(n+1). 22(n-1) cos x = 1 - 3 + - 6! + + (2(n − 1))! Here are requirements for the function m-file. - Parameter lists (inputs): 2 value (in radian), and desired error percentagel. - Return value (outputs): approximated value, real error percentage, and number of iterations - Function name:...
7. (5 points) Find the linear approximation for f(x) = tan(2x) at a = 0 and use it to approximate the value of tan(0.002). Hint: The linear approximation is just the tangent line to the curve at a = 2. 8. (5 points) Use the Mean Value Theorem for derivatives to find the value of x = c for f(x) = Vx on the interval (1,9). 9. (5 points) The acceleration of an object moving along the number line at...
TAYLOR POLYNOMIALS 1. LINEAR AND QUADRATIC APPROXIMATIONS Compute the linear approximation centered at a defined by L(x) = f(a) + f'(a)(x - a) and the quadratic approximation centered at a defined by Q(x) = f(a) + f'(a)(x - a) +- (x - a) 2 for the following functions when available: (a) f(1) = 23/2 with a = 1 (b) f(x) = V3 with a = 4 (c) f(x) = cos(x) with a = 7/4 (d) f(x) = x1/3 with a...
1. Linear Approximations. a. (40 pts) Find the linear approximation L(x) to the function f(x)tan(rx) at a (20 pts) Use the linear approximation to determinethe value at x = 0.4 at χ = 0.4, Compute the relative error: Then compare f(x) and L(x) LLarrul × 100% 1f(x)1 r(x)l
1. Linear Approximations. a. (40 pts) Find the linear approximation L(x) to the function f(x)tan(rx) at a (20 pts) Use the linear approximation to determinethe value at x = 0.4 at χ...
The function f that satisfies f'(x) = 3x2 +1, f(2)=5 is Select one: a. f(2)=23+ O b. f(x) = 2 + 1 - 5 O c. f(x)=x3 ++2 d. f(x) = 3x2 – 7 O e. None of these. Let f(2) be a function that is continuous on 1, 7] with f(1) =3 and f(7) = 9. Then the Intermediate Value Theorem guarantees that Select one: O a. f'(2)=1 has at least on solution in the open interval (1,7). O...
Let f(x,y)=x2y2+1.f(x,y)=x2y2+1. Use the Linear Approximation at
an appropriate point (a,b)(a,b) to estimate
f(5.02,1.91).f(5.02,1.91).
(Use decimal notation. Give your answer to two decimal
places.)
f(5.02,1.91)≈
Let f(x, y) = . Use the Linear Approximation at an appropriate point (a, b) to estimate f(5.02, 1.91). (Use decimal notation. Give your answer to two decimal places.) f(5.02, 1.91) - 4.59