Limits

Q1:
a)-1
b)loge1
c)1
d)none

q2:
a)12sin3a
b)12cosec2a
c)sin3a
d)cosec3a

q3:
a)1
b)-1
c)0
d)none

q4:if 0<x<y then
a)e
b)x
c)y
d)none

q5:
a)1
b)sinxx
c)xsinx
d)none

8 Answers

1357
Manish Shankar ·

first one

log(sinx)/1/x

Applying L'Hospital

cotx/(-1/x2)=-x2/tanx=-(x)(x/tanx)=0 as x->0

1357
Manish Shankar ·

fourth is

y(1+(xy)n)1/n

as x<y so (x/y)n will tend to zero

1357
Manish Shankar ·

For second one i m getting the (1-cosa)/(1-cota)

I think there's a mistake in the question..

it should be

lim (x->a)(cosx-cosa)/(cotx-cota)

1357
Manish Shankar ·

third one DNE

1357
Manish Shankar ·

Fifth one

divide and multiply by 2sinx2n and proceed

85
Anindita Roy ·

Sir how does the first one exist ?
M not understanding how lhl exists .. log of -ve is not defined . So sir where m i wrong ?

466
Himanshu Giria ·

1 D

466
Himanshu Giria ·

3 1

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