For the following exercises, find the values for each function, if they exist, then simplify. a. f ( 0 ) b. f ( 1 ) c. f ( 3 ) d. f ( − x ) e. f ( a ) f . f ( a + h ) 11. f ( x ) = 6 x + 5
For the following exercises, find the values for each function, if they exist, then simplify. a. f ( 0 ) b. f ( 1 ) c. f ( 3 ) d. f ( − x ) e. f ( a ) f . f ( a + h ) 11. f ( x ) = 6 x + 5
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Hwk 29
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Hwk 29 - (MA 244-03) (SP25) || X
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LARLINALG8 7.3.003.
Prove that the symmetric matrix is diagonalizable. (Assume that a is real.)
0 0 a
A =
a 0
a 0 0
Find the eigenvalues of A. (Enter your answers as a comma-separated list. Do not list the same eigenvalue multiple times.)
λ=
Find an invertible matrix P such that P-1AP is diagonal.
P =
Which of the following statements is true? (Select all that apply.)
☐ A is diagonalizable because it is a square matrix.
A is diagonalizable because it has a determinant of 0.
A is diagonalizable because it is an anti-diagonal matrix.
A is diagonalizable because it has 3 distinct eigenvalues.
A is diagonalizable because it has a nonzero determinant.
A is diagonalizable because it is a symmetric…
A polar curve is represented by the equation r1 = 7 + 4cos θ.Part A: What type of limaçon is this curve? Justify your answer using the constants in the equation.Part B: Is the curve symmetrical to the polar axis or the line θ = pi/2 Justify your answer algebraically.Part C: What are the two main differences between the graphs of r1 = 7 + 4cos θ and r2 = 4 + 4cos θ?
A curve, described by x2 + y2 + 8x = 0, has a point A at (−4, 4) on the curve.Part A: What are the polar coordinates of A? Give an exact answer.Part B: What is the polar form of the equation? What type of polar curve is this?Part C: What is the directed distance when Ø = 5pi/6 Give an exact answer.
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