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February 7, 2022 11:19 pm 30 pts
The limit lim _1) -0 xtan x 26. 32. Let Sa)= and define s(x) = f(x+1)-f(x). Then, as xo, the function g (x) converges to (a.) doesnot exist (b.) 9 (a.) 0 (c.) 0 (b.) 1 (d.) 3 (c.) e 27. The correct value of lim (d.) e x0 V1-cos x 33. Consider the functions f. g:Z>Z defined (a.) does not exist by f(n) = 3n+2 and s(n) =n' -5 (b.) is 2 (a.) Neither f and g is a one-to-one (c.) is-V2 function (d.) is 1/V2 (b.) The function f is one-to-one, but not g (c.) The function g is one-to-one, but notf 28. lim- equals non j=0 (d.) Both f and g are one-to-one functions 34. Let T be the graph of the function (a.) 4 1+x, -1 Sxs0; fa)1-x, 0SxS1 (b.) 16 (c.) 1 Then the reflection of T in the line y =0 is (d.) 8 given by the graph of s(x) where 29. If x and Y are two non-empty finite sets and f: X >Y and g:Y> X are mappings (a.) 8()1-1+x. -1-x,1šxs0 0srSl such that gof:X-X is a surjective (i.e., -1+x, -1srs0 (b.) 8(x)=-1-X, 0sxSl onto) map, then (a.) f must be one-to-one -1-X,1Sxs0 (b.) f must be onto (c.) 8)1-x, 0SxS1 (c.) g must be one-to-one l-x,-1Sxs0 d.)s()-1-X 0SxSl (d.) X and Y must have the same number of elements. 35. Let a,b,c.d be rational number with 30. Let P(x) be a non-constant polynomial such ad -bc # 0. then the function f:R\QR that P() = P(-n) for all ne N. Then P(0) ax+b (a.) Equals 1 is defined by f()=* cr+d (b.) Equals 0 (a.) onto but not one-one. (c.) Equals -1 (b.) one-one but not onto. (d.) Can not be determined from the given (C.) neither one-one nor onto. data. (d.) both one-one and onto. (1+2cxis 36. Let f:(0,o)> R be the function defined by If (1+ cx-4, then im-2cx) 31. o1-Cr 4, then lim+2cr ) S(x)=Then the lim f() (a.) 2 (a.) does not exist. (b.) 4 (b.) exists and is 0 (c.) 16 (c.) exists and is 1 (d.) 64 (d.) exists and is e 28A/11, (First Floor) Jia Sarai, Hauz Khas, Near I.I.T., New Delhi-110016, Ph.: (011)-26537527, Cell: 9999183434 & 9899161734, 85sss44789 175 please provide us the solutions of all the sums, sir
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