Each function f(x) changes value when x changes from x0 to x0 + dx. Find the change Δ.fX0 + dx)-foo), the value of the...
Assigned Each function f(x) changes value when x changes from Xo to xo + dx. Find the change Af = f(xo + dx) – f(xo), the value of the estimate df = f'(xo) dx, and the approximate error Af-df| f(x) = 4x2 - 5x, Xo = 2, dx = 0.1 The change Af=0. (Simplify your answer. Type an integer or a y=f Af = f + de) - doda of)) de Tangent о + de
The function f(x) changes value when x changes from xo to xo + dx. Find the change Af=f(xo + dx) = f(xo), the value of the estimate df = f'(x) dx, and the approximation error Af - dfſ. f(x) = 9x2 + 7%, * = 1, dx = 0.1 y = 0 T (T Af + d) - Mr) de ful Tangent 0 lue of Δf = (Type an integer or a decimal. Do not round.) df = 0 (Type...
(3 points) The figure shows how a function f (x) and its linear approximation (.e., its tangent line) change value when I changes from co to co + dr. y = f(x) fredr) Suppose f(x) = x2 + 2x, xo = 2 and dr = 0.05. Your answers below need to be very precise, so use many decimal places. (a) Find the change Af = f (30+ dc) - f(:30). Af Error = 14f-df Af = f(x + dr) -...
Given the function below f(x) = 3 – 45x3 + 72 Find the equation of the tangent line to the graph of the function at x = 1. Answer in mx + b form. L(x) Use the tangent line to approximate f(1.1). L(1.1) Compute the actual value of f(1.1). What is the error between the function value and the linear approximation? Answer as a positive value only. error (Approximate to at least 5 decimal places.)
6. Linear Approximation a. Suppose you have a function f(x), and suppose you know df|3 = −4 dx. What is the equation of the tangent line to y = f(x) at x = 3, if f(3) = 7? And give an estimate of f(2.8). b. The volume of a sphere of radius r is V = 1 3 πr3 . Find dV in terms of dr. Then find dV V in terms of dr r , and use it to...
Exam 2018s1] Consider the function f R2 R, defined by f(x,y) =12y + 3y-2 (a) Find the first-order Taylor approximation at the point Xo-(1,-2) and use it to find an approximate value for f(1.1,-2.1 (b) Calculate the Hessian 1 (x-4)' (Hr(%)) (x-%) at X-(1-2) c) Find the second-order Taylor approximation at xo- (1,-2) and use it to find an approximate value for f(1.1,-2.1 Use the calculator to compute the exact value of the function f(11,-2.1) Exam 2018s1] Consider the function...
Please answer all, be explanatory but concise. Thanks. Consider the function f(x) = e x a. Differentiate the Taylor series about 0 of f(x). b. ldentify the function represented by the differentiated series c. Give the interval of convergence of the power series for the derivative. Consider the differential equation y'(t) - 4y(t)- 8, y(0)4. a. Find a power series for the solution of the differential equation b. ldentify the function represented by the power series. Use a series to...
Question 2, non-calculator Question 1, calculator The curve C in the x-y-plane is given parametrically by (x(t), y(t), where dr = t sine) and dv = cos| t The Maclaruin series for a function f is given by r" for 1 sts 6 a) Use the ratio test to find the interval of convergence of the Maclaurin series for f a) Find the slope of the line tangent to the curve C at the point where t 3. b) Let...
15. . 16 . 17 Find a power series representation for the function. х f(x) (1 + 6x)2 f(x) = ( (-6).*- 1 nxt n = 0 x Determine the radius of convergence, R. R = 1/6 Evaluate the indefinite integral as a power series. t Vi dt 1 - 79 C+ Σ Σ( n = 0 What is the radius of convergence R? R= Use a power series to approximate the definite integral, I, to six decimal places. x3...
(a) Given constants C, a, 8 € R, define a function by z = f(x, y) = Crºy Let dx/a, dy/y, and dz/z be the approximate relative (percent) changes in x, y, and z, respec- tively. Find the relative (percent) change in z in terms of the relative (percent) changes of a and y. (b) The total production P of a certain product depends on the amount L of labour used and the amount K of capital investment. The Cobb-Douglas...