
Use the linear approximation method to estimate the value of ln (2.7^2) in terms of e
Quadratic approximation:
Cubic approximation:
2 near the origin Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y) = 7- x-V The quadratic approximation for f(x,y) is
2 near the origin Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y) = 7- x-V The quadratic approximation for f(x,y) is
For question 2 : Find the domain, y and x intercepts, f'(x),
f''(x), Maxima and minna, the table for increasing and
decreasing, table for concavity and then sketching
2. Draw the graph of f(x) = x In(\xD) - (x – 4) In(x – 41). 3. Use cubic approximation to estimate the value of ln(1.3).
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) =
11. Here is the Maclaurin series for f(x) = ln(1 +x2): Tm 1-1 r1/3 ln(1 +x2) dz to within 10-6). Use the series to estimate (i.e. 100000 o 0 Show your work and be sure to justify that your estimate has the required accuracy. Circle your estimate.
11. Here is the Maclaurin series for f(x) = ln(1 +x2): Tm 1-1 r1/3 ln(1 +x2) dz to within 10-6). Use the series to estimate (i.e. 100000 o 0 Show your work and...
(4) Use linear approximation to estimate tan-1(1.004)
(a) Estimate the value of tan(0.85) using a linear approximation. Let your point be a = use the fact that tan(x) = sec'(x)=- . Give the calculator value to 5 decimal dx cos? (x) places for comparison. (b) i. Give a reason that the function f(x x + x +5 has at least one zero. ii. Use the derivative to show that it cannot have more than one zero. Estimate the zero using 2 iterations of Newton's Method, if the...
Consider the initial-value problem yl =0.3y y(3) = 0.2 (a) Use Euler's method to estimate y (-2with step size h 0.5 Give your approximation for y (-2)with a precision of ±0.01 y(2) Number (b) Use Euler's method to estimate y (-2)with step size h = 0.25 Give your approximation for y (-2)with a precision of ±0.01 y (-2) Number
Consider the initial-value problem yl =0.3y y(3) = 0.2 (a) Use Euler's method to estimate y (-2with step size h 0.5...
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...
what approximation is used here? help
N ln (E + Δ)3/2 NIn E3/23 NA 2 E