SOLUTION: MATH 110 University at Albany Section 1 LHS and RHS Limit Calculus I HW

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Math 110 - Calculus I Section I- Multiple Choice Students Name Questions 1 and 2 relate to the diagram adown. y 4 3 2 1 x –3 –2 –1 1 3 2 –1 4 5 6 7 –2 –3 1. What is the compute of lim f (x) . x5 B. – 1 A. Does not await 2. What is the compute of C. 4 D. 1 E. Some other response C. 2 D. 1 E. Some other response lim f (x) . x1 A. Does not await B. – 1 x2 9 3. What is the compute of the lim x3 A. 6 B. 0 x 3 . C.  D. – 3 E. Some other response Page 1 x 4. 5. For what compute(s) of x is the exercise f(x) = 6. C. x = 1 and x = – 1 B. x = 1 D. x = 0 , x = 1 and x = – 1 E. Some other response 3 What is the compute of the aftercited proviso lim 4x 1 x2x 2 2 B. 0 C.  D.  B. ½ C.  D.  1 B. 0 C.  D.  2 8. E. Some other response 3 lim 2x 1 x4x3 2 What is the compute of the aftercited proviso A. E. Some other response lim 4x 1 x2x 2 What is the compute of the aftercited proviso A. 2 7. x 1 A. x = 0 A. 2  not normal? 2 The equation of the tangent cord to the incurvation y = 2 x  2 E. Some other response at the summit (1,0) is:- x 9. A. y = 2x – 1 B. y = 2x + 1 D. y = 2 E. Some other response C. y = 2x The equation of the tangent cord to the incurvation y = x3 – 5x + 3 at the summit (2,1) is:A. y = 8x + 13 B. y = – 9x – 13 D. y = –7x + 13 E. Some other response 10. What is the derivative of the exercise y = x   A. 1  2 x D. 1 2 x 1 2 x3  1  1 2 2 B. 1 2 x 1 x C. y = 7x – 13  2  1 2 x3 1  2 2 C. 1 2 x  1 2 x3 E. Some other response 2 x3 Page 2 11. The pose of a jot is loving by the formula s(t) = 1 cos (2 t) (delay t 0 ). 4 What is the acceleration when t = 5 A. B. 2 0 D. – 2 C. – 4 2 E. Some other response 12. What is the derivative of y = x2 e2x A. 2xe2x + x2ex B. 2xe2x + 2x2e2x D. xe2x + 2x2e2x E. Some other response C. xe2x + x2e2x t 2 1 13. What is the derivative of g(t) = t 1 t 2 t 1 A. 1 D. B. 2t t 2 t 1 C. E. Some other response t 12  14. What is the derivative of f(x) = sin( 2x 1) A. cos  2x 1  B. 2x 1  2x 1 D. cos t 12  2 cos 2x 1  2x 1  C. cos  2x 1  2 2x 1  E. Some other response 15. For h(x) = x3 + 5x2 – e4x what is h(x) the third derivative of h(x)? A. 6 – e4x B. 6 + e4x D. 6 – 64e4x E. Some other response C. 6 Page 3 16. The pose of a jot is loving by the formula s(t) = t3 – 1.5t2 – 2t (delay t 0 ). What is the acceleration when t = 5 A. 27 m/sec2 C. – 27 m/sec2 B. 35 m/sec2 D. – 35 m/sec2 E. Some other response 17. The pose of a jot is loving by the formula s(t) = 1 cos (2 t) (delay t 0 ). 4 What is the acceleration when t = 0 A. B. 2 0 D. – 2 C. – 4 2 E. Some other response 18. Use logarithmic differentiation to lump the exercise y = x6x. A. dy = x6x B. dx D. dy dy = 6x6x(6ln x + 1) dx = x6x(6ln x + 1) C. dy = 6x6x(ln x + 1) dx E. Some other response dx 19. For the exercise y = x what is the equation of the cordar bearing exercise at x = 4 A. y = 2 B. y = ¼ x C. y = ¼ x + 1 D. y = ¼ x + 2 E. Some other response 20. Experience the independent stint compute of y = x3 – 3x on the season [0,2]. A. 0 C. – 2 B. 2 D. – 3 E. Some other response 21. Experience all the exact total for f(x) = x4(x – 3)3 A. x = 0 , x = 2 and x = C. x = 0 , x = 3 and x = 12 7 12 7 B. x = 0 , x = 3 and x = D. x = 0 , x = 2 and x = 12 11 12 11 E. Some other response Page 4 22. On what season is f(x) = x4 – 6x2 excavated down. A. (– 1, 1) B.(0,1) C. (– 1, 0) D. ( , 1) E. Some other response 23. If f (1) = 0 and f (1) – 2 then which of the aftercited is a argumentative conclusion A There is a topical climax at x = 1 B There is a topical stint at x = 1 C There is a summit of inflexion at x = 1 D There is a perpendicular asymptote at x = 1. E. Some other response. 24. If f (x)  f(x) which one of the aftercited statements is penny. B. f(x) = ex + cx A. f(x) = x D. It is unusable for a exercise to have C. f(x) = ex + cx + d f (x) f(x) E. None of the statements are penny. 25. If f (x) 3x2 4x 1 and f(0) = 1 Then A. f(x) = x3 + 2x2 + 1 B. f(x) = x3 + 2x2 + x + 1 D. f(x) = 6x + 1 E. Some other response. C. f(x) = 6x + 4 26. If f (1) = 0 and f (1) – 2 then which of the aftercited is a argumentative conclusion A There is a topical climax at x = 1 B There is a topical stint at x = 1 C There is a summit of inflexion at x = 1 D There is a perpendicular asymptote at x = 1. E. Some other response. 27. Experience the independent climax compute of y = A. 10 B. 81 C. 8 81 x 2 on the season [– 9,9]. D. 1 E. Some other response 28. Experience f(x) when f (x) = 12x + 24x2 A. f(x) = 6x3 + 4x4 + cx + d B. f(x) = 2x3 + 2x4 + cx + d C. f(x) = 4x3 + 8x4 + cx + d D. f(x) = 2x3 + x4 + cx + d E. Some other response Page 5 Section II. In this individuality it is sharp to parade appropriate instituted as security can barely be loving for instituted that is paraden. You must as-well response using the regularity asked in those questions that state a point regularity. 1. Experience the aftercited provisos by algebraic resources – Do not use L’Hospitals Rule. (a) 2 lim x 4 x2 x 2 1 lim 1h (b) h0 h 2. By using provisos and primary principals experience f (a) for the exercise f(x) = x2 – x. Page 6 3. Draw a portray of y = f (x) by using the graph of y = f(x). y = f(x) 4. Lump the exercises:(a) f(x) = 2x3 + 4 + 2 x 4.(b) h(x) = 4 e x x2 Page 7 5. 4.(c) g(x) = 1 x2 4.(d) f(x) = sin3(2x + 1) 4.(e) h(x) = x3 4.(f) e x x g(x) = x e x Find dy x 2 1 for the exercise x2y2 + 4y = 5 by using indicated differentiation. dx Page 8 6. At noon ship A is 200 km west of ship B. Ship A is sailing north at 40 km/hour while ship B is sailing north at 25 km/hour. A 2 Give a formula for D in terms of x and y. (a) D x B y 200 km dx and dy , x , y and D when the duration is 6:00 p.m. (b) What are the computes of (c) What is the scold of diversify of the dissimilarity D between the ships at 6:00 p.m. dt dt 7. The magnitude of a round balloon is V = 4 r 3 . 3 Page 9 When the radius is 10 cm the radius is increasing at the scold of 2 cm/sec ( What is the scold of growth in the magnitude ( 8. dV dr 2) dt ) when the radius is 10 cm. dt A compatriot has 1000 feet of sheet; he wishes to environ a crosswise area, partitioned into 4 as shown adown. y x (a) Use the aloft knowledge to experience an countenance for y, in conditions of x. (b) Experience a mathematical formula for the area of the rectangle in conditions of x. (c) What compute of x gives the climax area for the aloft rectangle 9. Experience the provisos of the aftercited using L’Hospitals Rule. Page 10 (a) (b) 3 lim x 2 27 x3 x 9 4 lim x 2256 x 16 x4 (c) lim sin x cos x 1 x0 sin x cos x 1 (d) lim x ln(x) x0  10. The exercise f(x) = x3 – 3x + 7. Page 11 (a) For what seasons is the exercise f(x) increasing and decreasing? (b) Where are the topical max and min , if they await? (c) When is f(x) excavated up, excavated down and where are the summits of inflexion, if they await? 11. A compatriot has 100 feet of sheet, he can use a fabric on one edge but he must circumscribe the other three sides. What are the magnitude of the rectangle PQRS that has the highest area. S P y x Q R Page 12 12. The derivative f (x) cos x 4x 2 , if you are as-well told that f(0) = 2. Find a exercise f(x) that has all these properties. 13. Use the aftercited knowledge f (1) 2 , f (3) 6 g'(1) 1 , g'(2) 3 m(x) = f(x)g(x) , f (1) 4 and f (3) 10 g(1) 3 and g(3) 1 f (x) r(x) = and p(x) = f(g(x)) g(x) To experience m'(1), r'(1) and p'(1) Page 13 Page 14 ...
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