enigma

A function is given by, f(x)=e^-3x write down the third-order Taylor approximation for f(x) about x =0. Hence, evaluate f(0.258) giving your answer to 4 decimal places.

An initial-value problem is given by the differential equation, f(x,y) = x + y, y(0) = 1.64 The Euler-midpoint method is used to find an approximate value to y(0.1) with a step size of h = 0.1. Then use the integrating factor method, to find the exact val...

A function of two variables is given by, f (x,y) = 4x^3 + 7xy^4 - 5y^2 + 8 Determine, fxx + fyx at x = 4.25 and y = 3.69, giving your answer to 3 decimal places.

A function is given by, f(x,y) = x^4 - y^2 - 2x^2 + 2y - 7 Using the second derivative test for functions of two variables, classify the points (0,1) and (-1,1) as local maximum, local minimum or inconclusive.

i apologise if that is the case. it's just that i have no idea where to start. thank you for your time.

thanks for helping me. i was stuck trying to solve this.

i was going around in circles and putting the wrong values. thank you for your help. thanks.

(-1,1) is classified as a saddle point because the value it gives after the second derivative test is less than 0 therefore the value is inconclusive. While (0,1) is classified as a local maximum because the value it gives after the second derivative test...

after calculating the y' and y'' values. the values come up be 2.7731947639 which when rounded to 5 decimal places gives the answer as: 2.773195

after re-calculating the euler-midpoint method. the value I got was 1.8172 while using normal euler method is 1.968. however, I can't seem to find the exact solution to minus off the 1.8172 value to get the global error.