MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Range

If a,b∈ℝ and ...

Question

If $a, b \in R$ and $lim x \to 1 (a [x + 1] + b [x - 1])$ exists, then the value of $a + b$ is
$($ where $[.]$ denotes greatest integer function $)$

Open in App

Solution

$L . H . L . = lim x \to 1^{-} (a [x + 1] + b [x - 1]) = a - b R . H . L . = lim x \to 1^{+} (a [x + 1] + b [x - 1]) = 2 a$

$∵$ Limit exist
$L.H.L. = R.H.L. \Rightarrow a - b = 2 a ∴ a + b = 0$

Suggest Corrections

thumbs-up

3

Similar questions

a, b \in R

lim x \to 1 (a [x + 1] + b [x - 1])

exists, then the value of

a + b

[.]

denotes greatest integer function)

lim x \to 1 (2 - x + a [x - 1] + b [1 + x])

exists, then a and b can take the values (where [.] denotes the greatest integer function)

[x]

denotes the greatest integer function of

x

. If the domain of the function

\frac{1}{[x]^{2} - 7 [x] + 12}

R - [a, b),

then the value of

a + b

1 / 2 \int 1 / 8 [ln [\frac{1}{x}]] d x

\frac{a}{b},

a

b

are coprime, then the value of

b - 4 a

[.]

denotes the greatest integer function)

a = \sum_{n = 1}^{\infty} (\frac{2 n}{(2 n - 1)!})

b = \sum_{n = 1}^{\infty} (\frac{2 n}{(2 n + 1)!})

. Find value of [a] + [3b] where [ ] denotes greatest integer function or integral value of x.

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon