please do all 3 1. (3 points) Find the derivative of F(x) = (t +2) dt....
8. Find the derivative of F(x) = 322(t + 2) dt
3. (25 Points) Find f(t). f(0) + f(t - 1)f(t)dt = t. Hint: The second term on the left side is a convolution and it might be helpful to use the Laplace Transform. 1 4. (10 Points) Solve the initial value problem by Laplace transform techniques. x" + 5x' + 4x = 0;x(0) = 1,x'(0) = 0. I 5. (15 Points) Find a series solution for the following differential equation. Calculate the radius of convergence. 2(x - 1)y' = 3y...
Let F(x) = ſ vt(t+1) dt. Find F'(x) (again, the derivative!!). In()
3) Let F(x) = {* In In(1+t) dt. t (a) Find the Maclaurin series for F: (b) Use the series in part (a) to evaluate F(-1) exactly and use the result to state its interval of convergence. (c) Approximate F(1) to three decimals. (Hint: Look for an alternating series. )
57. Find the total derivative dz/dt, given (a) z = x^2− 8xy − y^3 , where x = 3t and y = 1 − t. (b) z = f(x, y, t), where x = a + bt, and y = c + k
1. (a) We want to develop a method for calculating the function sint dt f)-inf t 0 for small or moderately small values of x. This is a special function called the "sine integral", and it is related to another special function called the "exponential integral". It arises in diffraction problems. Derive a Taylor-series expression for f(x), and give an upper bound for the error when the series is terminated after the n-th order term. [HINT: (-1)"*z ? + R...
3. Find all critical points of dt dt with the constraint PP = 8 0 (c and boundary conditions x(0) - 0, x(1)- 3. Hint: Write the Euler Lagrange equation (there is no dependence on t), and then use the boundary conditions and the constraint to reach a system of 2 equations (with quadratic terms) of two unknown constants a, b Solve it by first finding a quadratic equation for a/b 3. Find all critical points of dt dt with...
Please solve the all questions. Thanks Probleml: Suppose that F(x) = $ f (Ed dt, where ! Find "(2). Carral Problen 2: Let y = f Use the fundamental Theoren 10t+ sin(tl) at of Calculus to find. using the fundamentul Find the derivative of the function Theoren of Calculus. F(x) = f (2 2-2) de Find & flxd dx if ft) = { t for I for X21. r for x> 1. z
1. (12 points) Find all the critical points of f(x) = (x - 1)(x + 5) Hint: Do not expand! Instead use the product and chain rules then factor 2. (12 points) Find the absolute extrema of f(x) = on (-1,2). Give your answers as (x,y) points. Hint: It is much easier to take the derivative of f(x) by rewriting as f(x) = (1 + x4)-1 and use the chain rule 3. f(x) = ? - 7x + 1 (a)...
[3 marks] d) Suppose f(x, y,z) x3yzxy +z 3; Given: x 3 cos t; y 3 sint; z=2; i. Finds ii. Evaluate it when t -0 for f(3,1,2) iii. Evaluate it when t for f (1,1,2) dt 13 marks] 3 marks]