Calculus ch#1 (5)
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#CivilEngineering #Calculus #Chapter #1 #Exercise 1-6 @Fully Solved Question #Related theory Further I am upload the remainning chapter step by step.
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81° Let fm = +1 Tfx > 1 @§>;'i/3"x .1 »~,y__ 5
Find f(1+0) and f(1-0). f ~
_ @ _m_&1_. .. _W
3 lf x S -2 ~.,~)’§ `-M65 .
32° f(x)= -“Ex” if-2<x<2
3 if x 2 2
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Find lim f (x) as x --> 2.
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34. Let f(x)= 1 _*_ 0
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Find limo f (x).
x2 if x S 1
35. Let f(x) =
x3 if x > 1
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36. Let f(x)= 2 _
ax 1fx > -1
Finda sothat lim f(x) exists.
x-»-1
Written by: Prof. Muhammad Farooq
Punjab College, Sargodha](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Calculus ch#1 (5)
- 1. EXERCISE 1.2 /Q(`fY ,WL-.Pan Evaluate the indicated limits (Problems 1 -30): -2 fi-1.1. 1' --" 2. 1' _ ~f * .Y-T2 `j2+x :Lili x`1 _ 1 3 3° ,Tl 1-x _ 1-x3 _ 4. If P,, (x) = a.,x"+a,x""+... +a,,_,x+a,,.,prove that lim ‘P,, (x) = P,, (a) I1)G _ cscx-cotx “_ sin ax.. hm ' -~ 6. hm f-r->0 x--10 sln bx_ 2/3_ 2/3 7. lim s./ um L-Lx->0 x y->x .y"x 9. lim igggil 6 10. lim xsin(l)x-»x slnx ’ x-->0 x- _ 2 lgflilno sin 12. rim” *-xx+-gl 13. lim 5’%“l 14. lim (1+3)‘x-¢°° x '5 x-->°° xx _ 1 I _ x 115.x2u¢_(1-x) 16. rlmm(*1+x) '/ :_ 4_ ~/iv. lim <a> 1) 18. lim %%-‘25-`foo W/.1~a x-a°° Written by: Prof. Muhammad Farooq Punjab College, Sargodha Notes of Chapter 01 Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Available at http://www.MathCity.org
- 2. x2 x2 .af _ _ ' -- -_ -- 20. l -] 2- 2 1? _,,&,n;.._ x+1 _x'+3 ,,l,m.. x a ) _ x2+1 . _» 5x’+3x’-1' 2* ,E_?°,.?f W ,l;”;.. 1' x-4x‘ _ 4 lim éiéf- Q Kim (x‘-x3+x) .fi-)°° I i’°° .> x2 xg Y . [ 3 2 #E ,2,“;,. ,TIE - m .»-ZF* ,i:,°;.. 4” -3* +°°~1] *JI-x2 x-1 2. 1° ~--- za. ~1° ---/1`>._lnf.0 1-I f- ¢;»I?.o jx2_1 X 3, _ 2 ' 129 lim --"-“4x 3l. lim -_*~x+smx "J x-v2-0 Q6-5x-Q-12 "" x---1°-= x . '. r x“+3 f x S 1 'DA 81° Let fm = +1 Tfx > 1 @§>;'i/3"x .1 »~,y__ 5 Find f(1+0) and f(1-0). f ~ _ @ _m_&1_. .. _W 3 lf x S -2 ~.,~)’§ `-M65 . 32° f(x)= -“Ex” if-2<x<2 3 if x 2 2 Find f(-21-0),'f1(-2+0).f(2-0) =mdf<2+o> x’-1 `if x S 2 _/~,>_ QL? f2~»..- 3 ,38..Let fm = Jze, w -5-"*“~_ _,f ]x+7 ifx > 2`"”‘"' ->/I' ""'-f1""!f/ Find lim f (x) as x --> 2. cosx ifx S 0 34. Let f(x)= 1 _*_ 0 -x 1 x > Find limo f (x). x2 if x S 1 35. Let f(x) = x3 if x > 1 Showthat lim f(x)= 1 x-al x+2 if x S - 1 36. Let f(x)= 2 _ ax 1fx > -1 Finda sothat lim f(x) exists. x-»-1 Written by: Prof. Muhammad Farooq Punjab College, Sargodha
- 3. Evaluate lim -Q-;Lx->3+0 I-3| Evaluate lim --£--x_~»o_o x-|x|. Find 'lim ----Lh->0-0 h r Evaluate, [ - ~ ~ ] being thebfacket function: (i) 1i1P'[2.x](x-1) -(ii) limo [x][x+1 (iii) 32210 1 (iv) ,BTO Available at http://www.MathCity.org Written by: Prof. Muhammad Farooq Punjab College, Sargodha
- 4. Available at http://www.MathCity.org Written by: Prof. Muhammad Farooq Punjab College, Sargodha
- 5. Available at http://www.MathCity.org Written by: Prof. Muhammad Farooq Punjab College, Sargodha
- 6. Written by: Prof. Muhammad Farooq Punjab College, Sargodha
- 12. Available at http://www.MathCity.org Written by: Prof. Muhammad Farooq Punjab College, Sargodha