Indicate if the following statement is TRUE or FALSE. Briefly justify your response with an explanation or a counterexample. If f is continuous at C and f(c) > 0, then there is a S> 0 so that for all o 0 in the O-neighborhood of c.

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A: We will use Laplace transformation table  f't  = s Fs− f0f'' t= s2 Fs − s f0 − f0Lsinat=aa2+s2

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A: The explanation is as follows

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Q: 14. Let A = {1,2,3,4,5,6} and p₁ = (4,2,5) and p₂ = (2,6,1) be permutations of A. Compute p₂¹P₁-1…

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Q: 2. Equip C[0, 1] with the inner product (f 19) = f(x) g(x) dr. Define the func- tions fi(1) = 1,…

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Q: 7. Prove that ||A|| = omax (A) for a real matrix A.

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Q: 08--00-- and W₂ = (a) Find a basis for W₁ W₂. What is dim(W₁ W₂)? (b) Show that R³ =W₁ + W₂- (c)…

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Q: 2. Given the following sequence: 4, 10, 22, 46, .... Write a recursive formula for the sequence.

A: Given some set of sequence i.e, 4,10,22,46 Lets find the recursive formula for this sequence

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A: 1. Given matrix is A=907-32-1241 R2→R2+13R1R3→R3-29R1 A=907024/304-5/9

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Q: What is the general solution of the following ODE * (x² + xy - y²) dx + (1²/7 -(x² - 2xy) dy = 0

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Q: Given polar curves A₁: r = 1 + sin 0 and A₂: r = 3 sin 0 1. Solve for the polar coordinates of the…

A: given  A1:r=1+sinθ and A2:r=3sinθ (1) solve for the polar coordinates of the intersections

Q: 4. (1 3 2 3 1 Given the matrix A 2 6 5 4 5 39785 (a) Find a basis each for N(A) and C(A). What is…

A: Given: Let us consider the given matrix, A=132312654539785 Let's determine, a) Basis for NA and CA…