Question

Finding a limit

Answer 1

\[\lim_{x \rightarrow 0} \frac{ \sqrt[5]{1+2x}-1 }{ \sin x }\]

Answer 2

try l`hopital

Answer 3

sorry, I forgot to mention that we haven't learnt about l`hopital

Answer 4

nvm

Answer 5

you learned Taylors series?

Answer 6

Nope

Answer 7

expand the root term by binomial theorem

Answer 8

then there will be term like
10x/sinx
and
x/sinx=1
for given condition
so ans =10

Answer 9

while opening with binomial neglect higher degree terms

Answer 10

well, the answer should be 0.4 . And what do you mean by expanding the root term by binomial theorem? Do you mean, that I should raise the fraction by the 5th degree and then use the binomial theorem and numerator?

Answer 11

no see it i have shown