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2nd - 2DU?—2CIC|8 FALL LIATH 119 WEEK 2 RECITATION...

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Unformatted text preview: 2DU?—2CIC|8 FALL LIATH 119 WEEK 2 RECITATION QUESTIONS 1} Prove lim [21: + 3:] = 5 using the E, 5 definition of limit and illustrate with a 3—H diagram. 1 2} Prove, using definition of infinite limits, that lim oo. m—r—l {I + 3}4 = 3} For what values of the constant c is the function 3‘ continuous on [—o-o, co] _ cr+1 ifIES Jill”)— erg—1 if:.-:>3 4} From the graph of g, state the intervals on which 9 is continuous. 5] Use the intermediate value theorem to show that there is a root of the equa— tion 34+ :1: — 3 = U in the interval (1,2). 6] Fin an equation of the tangent line to the curve y = 1321? + 1 at the point {4: 3}- ?) Sketch the graph ofa function f for which ffifl) = D, 3WD} = 3, f’fl] = I], and fl?) = —1- 8] Find rm} if fit} = % 9} Trace or copy the graph of the given function f. {Assume that the axes have equal scales.) Then use the method of Example 1 {in section 3.2} to sketch the graph of f’ belov.r it. }' 10} Find the derivative of the function fix) : 1 — 3;]:2 using the definition of derivative. State the domain of f and the domain of its derivative. 11] Differentiate the function 1: = t2 — 14%. 12} Differentiate F[y) 2 (gig — 3%) (y + 53.3}. 13} Find an equation of the tangent line to the curve y : f—E at the point [1, 1}. ...
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