cos ax- cos bx .2 3. Let f(x) = 3x0-7x+ 5x-21x+ 3x-7, then the HEMATICS r....
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cos ax- cos bx .2 3. Let f(x) = 3x0-7x+ 5x-21x+ 3x-7, then the HEMATICS r. MATHEMATICS %3D then value of Lt If f(x)= f(1-h)- f(1) 2 79. h-0 is h' +3h where a,b are real and district constants, then 50 1) 3 22 2) 3 2) f is continuous at x 0 lim f(x) does not exist 3) 1)f is discontinuous at x=0 3) 13 TC 13 sin+h-cos Lim2 TC +h 6. 4. 6. 4) flo) is not defined ANSWERS h→0 3.h//3 cosh-sinh then a -2- 1) -4 2) m and I, is 3) 3 4) 4 5) 1 3) 4 2) 2 1) 3 7) 4 811 8) 1 9) 3 10) 2 x2n -1 Let f(x) = Lt 5. 6) 1 %3D 11)1 12)4 13) 2 16) 1 17) 2 18) 4 21)1 22)4 23) 1 28) 2 14) 3 15) 2 2n n→o x" +1 then 19) 4 20) 2 1) (x) = 1 for lx = 1 %3D 24) 2 25) 4 | 1, for Ix>1 -1, for 1xk1 2) f(x) = %3D 26) 3 27) 2 29) 1 30) 1 31)2 32) 1 33)1 34) 1 35) 2 3 1, for \x>1 -1, for |x<1 38) 2 39) 3 40) 4 3) f(x) = 36) 1 37)3 3 18 %D 41) 2 42) 3 43) 1 44) 1 45) 1 4) f is not defined for any value of 'x' 46) 2 47)1 48) 1 49) 4 50) 4 TT 1 MGMI 4) 51)1 52) 1 53) 2 a 54)1 55) 3 Lim- 6. If a>1, then the value of V is 56) 2 57) 1 58) 2 59) 1 60)3 a +a' 61) 4 62) 2 63) 3 64) 2 65) 4 1) 1 2) 0 3 66) 4 67) 1 68) 1 69) 3 70) 3 3) 2 4) None of these 4) 71) 2 72) 2 75) 2 n 73) 2 74) 3 76) 2 77)4 78) 2 79) 1 Lim=1 n→2 7. r=1 X-2 2) (n-1)2"+1 LIMITS 1) n 4) (n-1)2"-1 3) (n-1)2" EXERCISE - |I Let a = min{x² + 2x + 3, xER} and Lab 8. 1. 1- cot x Lt .3 ty of f is 1- cose . The value of r=0 2-cot x- cot x 4. b = Lim 00 02 .3 %3D 2n+l 1 2n+l +1 2) 3.2" 4) 0 2) 3) 1) 3.2" 4n+l +1 4h+l -1 4) 3.2" TC Lt 1/x 4) 3 -1 tan 3) 3.2" %3D 109 1)0 4) e RACK CRD 2) 10 3) -1 is 8/3 4) 1/2 3/4 1/2 cos ax- cos bx .2 3. Let f(x) = 3x0-7x+ 5x-21x+ 3x-7, then the HEMATICS r. MATHEMATICS %3D then value of Lt If f(x)= f(1-h)- f(1) 2 79. h-0 is h' +3h where a,b are real and district constants, then 50 1) 3 22 2) 3 2) f is continuous at x 0 lim f(x) does not exist 3) 1)f is discontinuous at x=0 3) 13 TC 13 sin+h-cos Lim2 TC +h 6. 4. 6. 4) flo) is not defined ANSWERS h→0 3.h//3 cosh-sinh then a -2- 1) -4 2) m and I, is 3) 3 4) 4 5) 1 3) 4 2) 2 1) 3 7) 4 811 8) 1 9) 3 10) 2 x2n -1 Let f(x) = Lt 5. 6) 1 %3D 11)1 12)4 13) 2 16) 1 17) 2 18) 4 21)1 22)4 23) 1 28) 2 14) 3 15) 2 2n n→o x" +1 then 19) 4 20) 2 1) (x) = 1 for lx = 1 %3D 24) 2 25) 4 | 1, for Ix>1 -1, for 1xk1 2) f(x) = %3D 26) 3 27) 2 29) 1 30) 1 31)2 32) 1 33)1 34) 1 35) 2 3 1, for \x>1 -1, for |x<1 38) 2 39) 3 40) 4 3) f(x) = 36) 1 37)3 3 18 %D 41) 2 42) 3 43) 1 44) 1 45) 1 4) f is not defined for any value of 'x' 46) 2 47)1 48) 1 49) 4 50) 4 TT 1 MGMI 4) 51)1 52) 1 53) 2 a 54)1 55) 3 Lim- 6. If a>1, then the value of V is 56) 2 57) 1 58) 2 59) 1 60)3 a +a' 61) 4 62) 2 63) 3 64) 2 65) 4 1) 1 2) 0 3 66) 4 67) 1 68) 1 69) 3 70) 3 3) 2 4) None of these 4) 71) 2 72) 2 75) 2 n 73) 2 74) 3 76) 2 77)4 78) 2 79) 1 Lim=1 n→2 7. r=1 X-2 2) (n-1)2"+1 LIMITS 1) n 4) (n-1)2"-1 3) (n-1)2" EXERCISE - |I Let a = min{x² + 2x + 3, xER} and Lab 8. 1. 1- cot x Lt .3 ty of f is 1- cose . The value of r=0 2-cot x- cot x 4. b = Lim 00 02 .3 %3D 2n+l 1 2n+l +1 2) 3.2" 4) 0 2) 3) 1) 3.2" 4n+l +1 4h+l -1 4) 3.2" TC Lt 1/x 4) 3 -1 tan 3) 3.2" %3D 109 1)0 4) e RACK CRD 2) 10 3) -1 is 8/3 4) 1/2 3/4 1/2
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Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
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