(4) Consider the function f(x) = V2 cos x. (1) Find the linear approximation L to...
(1) True or False. Explain why or why not. Also, for each of (1)-(iv), graph f and L (if it exists) on one set of axes. (i) The linear approximation to f(x) = x2 at x = 0 is L(x) = 0. (ii) Linear approximation at x = O provides a good approximation to f(x) = (xl. (iii) If f(x) = mx + b, then the linear approximation to f at any point is L(x) = f(x). (iv) When linear...
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...
(2) Consider the function f(x,y) = cos y + sin y (a) Compute the local linearization of f(x,y) at (0,5). (b) Compute the quadratic polynomial for f(x,y) at (0,). (c) Compare the values of the linear and quadratic approximations in part (a) and (b) with the true values for f(,y) at the points (0.007,), (0,0.7924) and (0.7 ). Which approximation gives the closest values ?
letter d please 1. Given y = Vx+3. a) Find the linearization L (x) of the function at a = 1. (3pts) b) Find the linear approximation of the function at a = 1 and use it to approximate 13.98 an 4.05. Are these approximations overestimates or underestimates? Why? (5pts) c) Calculate Ay and dy (round to 3 decimal places) d) Sketch a diagram to show the line with x= 1 and dx = Ar=0.5. segments with length Ar=dx, Ay,...
1. Linear Approximation First, read Section 4.1 and the lecture notes of days 16 and 17. The steps for linear approximation of are as follows 1. Choose an objective function f whose value at r we want to estimate and choose a center value a closed to r 2. Compute the linearization L(x) - f(a)f'(a) (z - a) of the objective function 3. Compute L(x) to get the required approximation 4. Compute the second derivative and decide whether the linear...
Consider the function. f(x) = x (a) Find the inverse function of f. p-1(x) = 5V (b) Graph fand f-l on the same set of coordinate axes.
Consider the below wave function and answer the following questions. F(t) cos(T.6t)+cos(.5t) i) Graph the beat function for this wave. ii) What is the beat frequency? iii Calculate the proper sampling rate for this wave. iv) Calculate the time intervals between the samples. Consider the below wave function and answer the following questions. F(t) cos(T.6t)+cos(.5t) i) Graph the beat function for this wave. ii) What is the beat frequency? iii Calculate the proper sampling rate for this wave. iv) Calculate...
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...
(a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the linear approximation for f(x) around a = e and use this to approx- dy Hence, e T,y 5 marks imate f(3). markS (b) Evaluate the following limits. Simplify your results if possible. 5 marks 5 marks] lim cot 5x sin 6x cos 7a (i) (ii) limIn (a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the...
write the equation of the line that represents the linear approximation to the following function at the given point a. answer a, b and c. a. Write the equation of the line that represents the linear approximation to the following function at the given point a b. Use the linear approximation to estimate the given quantity approximation - exact C. Compute the percent error in the approximation, 100. where the exact value is given by a calculator exact f(x) =...