Question

Can anyone solve this? lim (x^2-x+1)/(x-sin(x)), x→0+. The answer is ∞. Please give me a step-wise solution.

Answer 1

first substitute 0 in place of x. you'd get
\[\left[ \frac{ 1 }{0}\right] =\frac{ + }{ }\infty\]
you see that x goes to zero from right side, so substitute a number which is near zero from right side, for instance 0,1 to determine the sign of that infinity. after doing that:
\[\frac{ 0,91 }{0,1-0,0017 }\]
you know that this value will be positive so the limit is + infinity

Answer 2

Can it be simplified first? And after that we can subsitute 0?

Answer 3

It won't give you anything cause x goes to zero, even if you factored x , you'd get sinx/x goes to one but upstairs 1/0 which you don't know if it's + or - infinity

Answer 4

okay! i got it. thanks for help.

Answer 5

yw:)

Answer 6

you are maths student?