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Quiz 11 - Math 1A, section 103
1. Let g(x) = 1∫x f(t)dt, where f is the function whose graph is shown.
(a) Evaluate g(0), g(1), g(2), g(3), and g(6).
(b) On what interval is g increasing?
(c) Where does g have a maximum value?
(d) Sketch a rough graph of g.
Jane works due north of home. Her husband Ben works due east. They leave for work at the same time. By the time Jane is 3 miles from home, the distance between them is on mile more then Ben's distance from home. How far from home is Ben?
Let T : V → W be a surjective linear map. For a subspace U ⊆ V, define the restriction T|u ∈ L (U, W) by T|u (u) = T (u) . Prove that there exists a subspace U of V such that T|u is an isomorphism.
What are the two steps for simplifying radicals? Can either step be deleted? If you could add a step that might make it easier or easier to understand, what step would you add? Please give an example.
G is a finite group with elements a and b. Let the conjugacy classes of these elements be A and B respectively and suppose |A|^2, |B|^2
Find convergence of newton raphson, regula falsi, secant and iterative method?
What are the projections of the point (2,3,5) on the xy, yz, and xz planes? Draw a rectangular box with the origin and (2,3,5) as opposite vertices and with its faces parallel to the coordinates planes.
Is the series geometric or telescoping? What is the nth partial sum sn? Is the series convergent or divergent? Why?
Compute the centripetal force acting on the body.
What is the number in cell A3? Use mental math to find the sum of each row, column, and diagonal. What did you discover about all of the sums?
What is the probability that he obtains a four -digit number less than 3265? A child takes four of the card and places them in some order.
Give a sketch of the graph of the function V(t). Your graph can be a "rough draft" and evaluate the value of the fax machine in years 0, 1 and 4. to the nearest tenth.
What are the possible orders of subgroups of S4? Prove that S4 has at least one subgroup of each of these orders. What are the elements of these subgroups?
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