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5. HOMEWORK. In each problem start with graphing a given function to get an idea what is going on. Desmos would be quite helpful here. ( 1) Explain in words why each of the following integrals is improper. (a) f2mt7e'zdt. ) [3: sec t dt. (b (C) If {El'2' (d) f121n(t 1)dt. (2) (a) Graph 3; = l/tl'l and y = 1/5\". Select two viewing windows (a) [0,10] X [0.1], (b) [0,100] x [0.1]. (0) Evaluate 11100 t% and fllm 5%. (d) Find ff\" {1% if it exists. What does this integral represent? Find ff\" 3%.; if it exists. (3) Determine whether each integral is convergent or divergent. If it is convergent evaluate it. (a) If\" e'zzdx. (b) 2 dz rho1)? (C) 1 7; (4) Explain why In 3: lnx dm IS improper. Evaluate 1t usmg the limit of a proper integral. (5) Calculate work needed to take a pixel 6 phone from the surface of the Earth to innity. Google needed constants and parameters