1.Suppose that the sequence (an) is monotone. Prove that {an} converges if and only if {a} converges. Show that the result does not hold without the monotonicity assumption.

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Q: Recall that Σ· i=1 i = n(n+1) 2 (a) Use the above formula (not induction) to find and prove a…

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Q: d 3 kilom is located

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Q: Find the conic equation which satisfies the separable differential equation dy/dx=−18x/y  with the…

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Q: 1. 2. Generate a random 4 by 4 matrix A with rank 4. Generate a random column vector b with 4…

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Q: 4. Suppose G=H₁ x x H₁ (where n 2 2). Show that if 1 ≤i<j≤n, then H, H, (e), where e is the neutral…

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Q: 4. Find the centroid of the solid bounded by y = x² and y = x if it was revolved around the y-axis.

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Q: 6. Find the velocity at any time t of a 6 kg of box free-falling against air resistance of 0.005 v…

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Q: ₂ F₁ ( 1 , ² ; ²³ ; x ² ) = — sin¯¹ x -1 (b) 2 F₁ ( 1 , ¹ ; 23 ;-x²) = -—- tan-¹ X

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Q: Show that the following data can be modeled by a quadratic function. x 012 3 4 P(x) 6 8 12 18 26…

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Q: A spring with an 8 kg mass is kept stretched 0.4 m beyond its natural length by a force of 32 N. The…

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Q: 4. Show that the following matrices do not form a basis for M22 2-2 B = 2017] 5. Find a polynomial…

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Q: For each 6-subset of (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14), give the next largest 6-subset…

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Q: 1. Evaluate the following commutators: a) [p, x5] b) [cos kx, p]

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Q: 2. Use the trapezoid rule and h = /4 to approximate the integral = √™1² si How small does h have to…

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Q: = You see Michael and Nikita agree on a secret key using the Diffie-Hellman key exchange. Michael…

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Q: 4. Assuming that the domain of each of the following functions is the largest possible subset of R,…

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Q: Find the orthogonal trajectories of the family of curves. Graph several members of each family on a…

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Q: B-N and u Compute the distance d from y to the line through u and the origin. Let y = d= 4 1 3 -4

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Q: Bad Düfed day. Co si.......

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Q: + (sint)j +t²k for 0≤t≤3 r(t)=(cost)i F(t)=(Int)i + (21)j +1²k for 1st ≤4

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Q: A frozen yogurt store has 11 toppings to choose from. In how many ways can 3 of the 11 toppings be…

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Q: What is minor M33 when the determinant is evaluated using the 3rd column in 12 1 0 3 1 2 14 3 1 23…

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Q: Let In the current question we'll evaluate the integral of f(2) along two separate curves by using…

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Q: How many 13-card bridge hands can be chosen from a deck of cards?

A: There are 52 cards in a deck of cards. 13-card bridge hands consist of 13 cards from the deck. Now,…

Q: 20 7. Consider the sequence 1, 3, 2, 1, 2,. a) List the next two terms of the sequence. Enter…

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Q: B All Ⓒ (i), (iii) D None E (i), (ii), (iv) (ii), (iii) Which of the following are true ? (i): R=…

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