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Question 1 (6 points) + - + f(x) -4 + - - + + - ...

Question 1 (6 points) + - + f(x) -4 + - - + + - f'(x) -5 -3 -1 1 4 - + - + + - + - f" (x) -4 -3 -2 -1 1 3 Given the sign charts of f.f' and f" above, answer the following questions. Note that each of the dotted dividing lines correspond to zeros of the cor...

Question 1. Find the Laplace transformation of functions [0,...

Question 1. Find the Laplace transformation of functions [0,00) R. Find the domain of transformed functions. a) f1(t)=sin(wt) . cos(wt), , w> 0 b) f2(t) = tcos(t) + e (3t) 4t, 0 t < TT = t TT Question 2. Find the inverse Laplace transformation of functions a) b) c) =

Exercise 3. In R³, we consider the following three vect...

Exercise 3. In R³, we consider the following three vectors: 1 2 6 1 = 1 v 2 = and 73 = 2 , 4 2 -5 (1) Prove that B = {71, U 2, of 3} is a basis of R³. (2) Using the Gram-Schmidt orthonormalization process. transform B into an orthonormal basis B' of R³. (3) Compute ...

Exercise 1. ( 3 A = 4 - 1 ) (1) Compute the eigenvalue...

Exercise 1. ( 3 A = 4 - 1 ) (1) Compute the eigenvalues of A and draw the eigenspaces of A in the xy plane. (2) Is the matrix A diagonalizable? Explain why. (3) Compute the angle between the eigenspaces of A. (4) Is it possible to find an orthonormal basis of eigenvectors of A? Explain t...

1. 0.66/1 points | Consider a finite population with five e...

1. 0.66/1 points | Consider a finite population with five elements labeled A, B, C, D, and E. Ten possible simple random samples of size 2 can be selected. (a) List the 10 samples beginning with AB, AC, and so on. (Enter your answers as a comma-separated list.) AB,AC,AD,AE,BC,BD,BE,CD,CE,DE (b) ...

PART A Question 1 1. Differentiate the following functions...

PART A Question 1 1. Differentiate the following functions: (a) ((x)=-4x2 = + 3x - 1 (c) h(x) = 3e* 'vx' + 1 [30 marks) 2. For function f(x) in 1a, write down the difference ratio at (equivalently indicated with or, and show that the limit for the increment going to zero is equal to the de...

1) The following data are a random sample from a normal dist...

1) The following data are a random sample from a normal distribution of rainbow trout length and weight. For the LENGTH data: a. Calculate the MLE of the mean and variance of the distribution b. Calculate the 95% confidence interval for the mean. c. Calculate the 95% confidence interval for...

1) Evaluate (1) _____ ∫1π₯2cos(1π₯)ππ₯ (π΄) 1...

1) Evaluate (1) _____ ∫1π₯2cos(1π₯)ππ₯ (π΄) 1π₯sin(1π₯) (π΅) −1π₯sin(1π₯)+πΆ (πΆ) sin(1π₯)+πΆ (π·) −sin(1π₯)+πΆ (πΈ) ππππ ππ π‘βπ ππππ£π 2) Solve the initial value problem (2) _____ ππ¦ππ₯=1√...

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