12/09/2014
Section 15.2 Follow up exercise
| Q3. Lim x→2    (x3/3 – 7x2) Lim x3/3   – 7 limx2 ,,    = (2)3/3 –   7(2)2 = 8/3 –   28  ,, = 8-84/3 ,, = -76/3 ,, = 251/3 | Q4. Lim x→3    2X-8/X+4 = 2limx – lim8/   limx + lim4 = 2(3) – 8/   3+4   = 6-8/7    = -2/7 | 
| Q5. Lim x→2      2X2  + 3/ X3 + 4X -2 = 2limx2  + lim3/ limx3 + 4limx – lim2 = 2(2)2  + 3/(2)3 + 4(2) – 2 =   8+3/8+8-2  =         11/14 | Q8. Lim x→-10       X2+25/X = limx2 +   lim25/ (-10) = (-10)2  + 25/ -10   ,,    100+25/-10 = 125/-10    ,,     = -12.5 | 
| Q12. Lim x→2    (5X3  + 10X2) = 5limx3  + 10limx2 = 5(2)3  + 10(2) ,,       5(8) + 10(4) = 40 +40    ,,     =    80 | Q13. Lim x→5     4X-20/3X2  – 7x +5 = 4limx –   20lim/ 3limx2 – 7limx +5lim =4(5) – 20/   3(5)2 – 7(5) + 5 =20-20/75-35+5   ,,      0/45 undefined | 
| Q14. Lim x→-2        10+x2/5-8x   + 2x2 = 10lim +limx2/5lim   – 8limx + 2limx2 = 10 + (-2)2/   5 – 8(-2) + 2(-2)2 = 10+4/ 5+16+8 = 14/29 | Q16. Lim x→5  [(x+3/x+6) (x2-12)] = [(limx+3lim/limx+6lim) (limx2-12lim)] =   (5+3/5+6) (52- 12)   ,,   (8/11)(25-12) =   (8/11)(13)     ,   = 9.45 | 
| Q17. Lim x→ -4    x2+8x-14/   2x+7 = limx2+8limx-14lim/   2limx+7lim = (-4)2  + 8(-4) – 14/2(-4) +7 =   16-32-14/-8+7     ,,   = -30/-1      ,,   = 30/1 | Q18. Lim x→1      x2+3x-24/x-3 =limx2+3limx-24lim/limx-3lim = (1)2 +3(1)   -24/1-3   ,,    = 1+3-24/1-3 = -20/-2   = 20/2      =      10/1 | 
| Q19. Lim x→-4    X2-16/x+4 (x)2  – (4)2/x+4    ,,   = (x+4)(x-4)/ x+4 = x-4   ,,      (-4)-4       ,,   = -8 | Q20. Lim x→ -9     81-x2/   9+x =(9)2  – (x)2 / 9+x     ,,   = (9+x) (9-x)/ 9+x) =   9-x     = 9-(-9)       = 18 | 
Two point formula example 25 page no. 685
Slope(m)   = ∆y / ∆x    = y2 – y1 / x2– x1
After 1 hour (example 25)
d = f(t) = 8t2+ 8t
d = f(1) = 8(1)2 +8(1)
d= f(1) = 8+8   = 16(after 1 hour) and 48 after 2 hours.
How much change is = y2 – y1/ x2 – x1 ,,   = 48-16/ 2-1   =   32/1     =  32 change in y due to change in x
 



 
 
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