limits

1.evaluate

\lim_{x\to2-} [x-3]/[x(square)-4]

26 Answers

106
Asish Mahapatra ·

Q1. lim(x→2-) (x-3)/(x2-4)
as x → 2- i.e. it is less than 2 so, x-3 <0 and x2-4<0
further x-3→ -1 and x2-4 → 0- So, if u divide u'll get -1/0- (both negative) hence lim = +∞

1
rahul wadhwani ·

hey ans are

1 ∞ 2 -∞ 3 ∞ 4 ∞ 5 -∞ 6 6
i think this as the answer wats the correct one

1
rickde ·

getting same ans as celestine . use graphs sab aasan ho jayega

6th me direct value put karna

9
Celestine preetham ·

ans are

1 ∞
2 -∞
3 ∞
4 ∞
5 -∞
6 6

106
Asish Mahapatra ·

mani. limit will exist. he has specified -2+ or -8+ or 0+ or 0-

11
Mani Pal Singh ·

sorry guys
god work asish
but i am afraid u r wasting ur time as IIT or AIEEE people will never fight over ifinity
The answer to ur questions ANAND is the limit does not exist

1
JOHNCENA IS BACK ·

arey it is -a+ means the right hand limit at -a
and vice versa

106
Asish Mahapatra ·

now even i have got confused
what is -a+ ?
is it -(a+) i.e. if a = 2 is it -2.00000000001
or is it (-a)+ i.e. if a=2 is it -1.9999999999

1
JOHNCENA IS BACK ·

in 3rd one

if we take lim(h-0)f(-pi/2+h)..........we get infinity.................[11]

plz tell mistake

1
JOHNCENA IS BACK ·

hey in 1st ne i m doing like this:

taking lim(h- 0) f(2-h)............and getting -infinity............[11]

1
JOHNCENA IS BACK ·

3rd one ans. given is -infinity

106
Asish Mahapatra ·

Q5. lim(x→ 0-) 1+cosecx
As x is in 4th quadrant and tending to zero, hence cosecx tends to -∞ hence the limit is 1+(-∞) = -∞

Q6. if f(x)=3(x+1),x>0
lim(x→1) f(x) = lim(x→1) 3(x+1) = 3(1+1) = 6

106
Asish Mahapatra ·

Q2. lim(x→ -8+) 2x/(x+8)
here denominator tends to 0+ (i.e. positive) as numerator is negative tending to -16 so the limit is -∞

Q3. lim(x→ -π/2+) secx
sec(-π/2+) +∞ as the angle comes is in the 4th quadrant

Q4. lim(x→ 0-) 2-cotx
as x is in 4th quadrant and tending to zero, hence cotx = -∞
So, the limit is 2-(-∞) = 2+∞ = ∞

1
JOHNCENA IS BACK ·

\lim_{x\to-8+}[2x/(x+8)]

1
ayush211992 srivastav ·

hei in first one apply componendo and dividendo
and then put the limit

1
JOHNCENA IS BACK ·

VECTOR POST UR SOLUTION TO CLARIFY WAT DO U MEAN!

1
vector ·

johncena how cud u getminus infinite
ull get minus in both numerator n denominator

1
JOHNCENA IS BACK ·

FOR 1ST ANSWER IS GIVEN INFINITY [BUT ME GETTING -INFINITY]

1
prateek punj ·

yaar for sure 1) ka toh limit doesn't exist

x cann't be equal to 2....so f(2) does n't exist......

1
JOHNCENA IS BACK ·

@#7 AND #9

ANS. GIVEN DIFFERS

I M GETTING 1.-INFINITY 2.-INFINITY

1
Manas ·

2nd is -16

1
JOHNCENA IS BACK ·

i request everyone to plz post solutions too

1
JOHNCENA IS BACK ·

if f(x)=3(x+1),x>0

find \lim_{x \to 1}f(x)

1
JOHNCENA IS BACK ·

\lim_{x \to 0-}1+cosecx

1
JOHNCENA IS BACK ·

\lim_{x \to 0-}2-cotx

1
JOHNCENA IS BACK ·

\lim_{x \to -pi/2+}secx

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