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Statement-1 : lim(xrarr oo) ((x+1)^10+...

Statement-1 :
`lim_(xrarr oo) ((x+1)^10+(x+2)^10+.....+(x+100)^(10))/(x^10+9^10)` =100
Statement -2 : If `f(x)and g(x) ` are polynomials of same degree, then `lim_(xrarroo) (f(x))/(g(x))=("Coefficient of leading term in" f(x))/("Coefficient of leading term in" g(x))`

A

Statement -1 is true, Statement-2 is true,, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for statement -1.

C

Statement-1 is true, Statement-2 is False.

D

Statement-1 is False, Statement-2 is true.

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly, statement-2 is true (See Theory on page 34.9) .
Now,
`lim_(xto oo) ((x+1)^10+(x+2)^10+.....+(x+100)^(10))/(x^10+9^10)`
`=lim_(xtooo) (100x^100 +.^10C_1(1+2+.....+100)x^9+.....+(1^10+2^10+......100^10))/(x^10+9^10)`
`=(100)/(1)=100` [Using statement -2]
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