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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