Asked by sushma
1)lim [(x+y)sec(x+y)-xsecx]/ y
x-o
2)show that lim |x-4|/x-4 does not exists
x-4
3)lim [1-sinx/2]/[cosx/2{(cosx/4)-
x-22/7 (sinx/4)}]
x-o
2)show that lim |x-4|/x-4 does not exists
x-4
3)lim [1-sinx/2]/[cosx/2{(cosx/4)-
x-22/7 (sinx/4)}]
Answers
Answered by
Steve
#1: If you mean x-->0, then take a look at what that leaves:
y secy / y = secy
#2: |x-4| = x-4 if x > 4
|x-4| = -(x-4) if x < 4
so, the limit from the left and right are different.
#3:
lim x-->pi
[1-sinx/2]/[cosx/2{(cosx/4)-(sinx/4)}]
what if x = pi? we have
[1-1]/[(0)(0)] = 0/0, so let's try lHospital's Rule:
-1/2 cos x/2
-----------------------
1/2√2 (sin(pi-x)/4) (3sin x/2 + 1)
-1/2
------------
1/2√2 (0)(4)
= -oo
y secy / y = secy
#2: |x-4| = x-4 if x > 4
|x-4| = -(x-4) if x < 4
so, the limit from the left and right are different.
#3:
lim x-->pi
[1-sinx/2]/[cosx/2{(cosx/4)-(sinx/4)}]
what if x = pi? we have
[1-1]/[(0)(0)] = 0/0, so let's try lHospital's Rule:
-1/2 cos x/2
-----------------------
1/2√2 (sin(pi-x)/4) (3sin x/2 + 1)
-1/2
------------
1/2√2 (0)(4)
= -oo
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.