- #1

- 212

- 0

A)

lim x/|x|

x→ 0

limit does not exist

B)

lim [(x^2)-1]/(x-1)

x→ −1

=(1-1) / (-1-1) = 0/-2 = 0

c)

lim [(x^2)+4x−5]/[(x^2)+x−2]

x→ 1

= (x+5)(x-1)/(x+2)(x-1) = (x+5)/(x+2) = 6/3 = 2

d)

lim |x|

x→ 0

= 0

e)

lim [(2t^2)−3t−2]/[(t^2)+t−6]

t→ 2

= (2t+1)(t-2) / (t+3)(t-2) = (2t+1)/(t+3) = 5/5 = 1

f)

lim[(x^2)−2x+1]/[(x^2)−1]

x→ 1

= (x-1)(x-1) / (x-1)(x+1) = (x-1)/(x+1) = 0/2 = 0

g)

If f(x)=2x−7 find

lim (f(x+h)−f(x)) / h

h→ 0

=2(x+h)-7 - (2x-7) / h

= 2x + 2h -7 - 2x + 7 / h

= 2h / h = 2

h)

If f(x)=(2(x^2)+3x+5) find

lim (f(h)−f(0) )/ h

h→ 0

=2(h^2) + 3h +5 -5 / h

=h(2h+3) / h

=2h+3 = 3

i)

If f(x)=(−25) / (2x+3)

find

lim [f(1+h)−f(1)] / h

h→ 0

= (25/ 2(1+h) +3) - (25/ 2(1) + 3) /h

= (25/ 5+2h) - (5) / h

= (25/ 5+2h) - (5(5+2h))/(5+2h) /h

= (25-25-10h)/(5+2h) /h

= -10 / 5+2h

= -2

j)

lim [(x^2)+h] / [x+(h^2)]

h→ 0

= (x^2) / x

= x

Thanks