CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If $$\displaystyle \lim_{n \rightarrow \infty} \displaystyle \left ( an - \frac{1 + n^2}{1 + n} \right ) = b$$, where a and b are finite numbers, then


A
a=1
loader
B
a=0
loader
C
b=1
loader
D
b=1
loader

Solution

The correct options are
B $$ b = 1$$
C $$a = 1$$
$$limit \displaystyle = \lim_{n \rightarrow \infty} \frac{an ( 1 + n) - (1 + n^2)}{1 + n}$$

$$=\displaystyle  \lim_{n \rightarrow \infty} \displaystyle \frac{(a-1) n^2 + an - 1}{n + 1}$$

$$= \infty $$ if $$ a - 1 \neq 0$$
If $$ a- 1 = 0$$, limit $$=\displaystyle  \lim_{n \rightarrow \infty } \displaystyle \frac{an - 1}{n + 1} = a = b$$
$$\therefore a = b = 1$$

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image