I have been given a series of limits to evaluate, where I can only know if I got 100% of them correct or not, as opposed to individually. So, I'm not sure which I have made a mistake on, so I will post all the limits and my work. Thanks(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Evaluating Limits

**Physics Forums | Science Articles, Homework Help, Discussion**