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Question
`lim_(x→0) (sin^2x)/(sqrt(2) - sqrt(1 + cos))` equals ______.
Options
`sqrt(2)`
`4sqrt(2)`
4
`2sqrt(2)`
MCQ
Fill in the Blanks
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Solution
`lim_(x→0) (sin^2x)/(sqrt(2) - sqrt(1 + cos))` equals `underlinebb(4sqrt(2))`.
Explanation:
`lim_(x→0) (sin^2x)/(sqrt(2) - sqrt(1 + cos))` `(0/0)`form
'L' Hospital Rule
`lim_(x→0) (2sinxcosx)/(0 - 1/2 ((-sinx))/sqrt(1 + cosx))`
= `4sqrt(2)`
shaalaa.com
Limits Using L-hospital's Rule
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