Evaluate Lt of x^2-√x÷√x-1 when x approaches 1.

Asked by shaktidevgun | 5th Dec, 2015, 03:53: PM

Expert Answer:

W e space n e e d space t o space e v a l u a t e space t h e space l i m i t space stack l i m with x rightwards arrow 1 below fraction numerator x squared minus square root of x over denominator square root of x minus 1 end fraction colon T h u s comma space stack l i m with x rightwards arrow 1 below fraction numerator x squared minus square root of x over denominator square root of x minus 1 end fraction equals stack l i m with x rightwards arrow 1 below fraction numerator x squared plus x square root of x plus x minus x square root of x minus x minus square root of x over denominator square root of x minus 1 end fraction space space open square brackets a d d i n g space a n d space s u b t r a c t i n g space t e r m s comma space x square root of x space space a n d space x close square brackets space space space space space space space space space space space space space space space space space space space space space equals stack l i m with x rightwards arrow 1 below fraction numerator open parentheses x minus square root of x close parentheses open parentheses x plus square root of x plus 1 close parentheses over denominator square root of x minus 1 end fraction space space space space space space space space space space space space space space space space space space space space space equals stack l i m with x rightwards arrow 1 below fraction numerator square root of x open parentheses square root of x minus 1 close parentheses open parentheses x plus square root of x plus 1 close parentheses over denominator square root of x minus 1 end fraction space space space space space space space space space space space space space space space space space space space space space equals stack l i m with x rightwards arrow 1 below square root of x open parentheses x plus square root of x plus 1 close parentheses space space space space space space space space space space space space space space space space space space space space space equals square root of 1 open parentheses 1 plus square root of 1 plus 1 close parentheses space space space space space space space space space space space space space space space space space space space space space equals 3

Answered by Vimala Ramamurthy | 5th Dec, 2015, 04:46: PM