Question

please solve this question for me.
Class XI,maths, limit​

Answer 1

ANSWER

4

EXPLAINATION

FORMULA

$lim_{x - > \: 0}( \frac{ log(1 + x) }{x} ) = 1$

CALCULATION

$lim_{x - > \: 0}( \frac{ log(1 + 4x) }{x} )$

Let us substitute 4x =y i.e. x = y/4

When x -> 0, y -> 0

Therefore the limit becomes

$lim_{y - > \: 0}( \frac{ log(1 + y) }{ \frac{y}{4} } )$

$= lim_{y - > \: 0}( \frac{ log(1 + y) }{y}.4 )$

$=4 lim_{y - > \: 0}( \frac{ log(1 + y) }{y} )$

$= 4 \times 1$

$= 4$