Explanation for the correct option:Evaluating the limitlimit_x→∞sin(x)/xwhen we substitute limit it becomes the value sin(∞)/∞ where sin(∞)∈[ 1,1]=[ 1,1]/∞0ex0e ...

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

Byju's Answer

Standard XI

Mathematics

Differentiability

limitx→∞sinx/...

Question

$l i m i t_{x \to \infty} \frac{\sin (x)}{x} =$

$\infty$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$1$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$0$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

does not exist

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
$0$

Explanation for the correct option:
Evaluating the limit
$l i m i t_{x \to \infty} \frac{\sin (x)}{x}$
when we substitute limit it becomes the value $\frac{\sin (\infty)}{\infty}$ where $\sin (\infty) \in [- 1, 1]$
$= \frac{[- 1, 1]}{\infty} = 0 \times [- 1, 1] [∵ \frac{1}{\infty} = 0] = 0$
Hence, option (C) is the correct answer

Suggest Corrections

Similar questions

Q. The function f(x) = cot⁻¹ x + x increases in the interval
(a) (1, ∞)
(b) (−1, ∞)
(c) (−∞, ∞)
(d) (0, ∞)

Q. The set of points where the function f (x) = x |x| is differentiable is
(a)

(- \infty, \infty)

(b)

(- \infty, 0) \cup (0, \infty)

(c)

(0, \infty)

(d)

[0, \infty]

If $| x + 3 | \geq 10$ ,then

Q. If

f (x) = x^{2} + 1

and

g (x) = 2 x

, then find the domain of the function

h (x) = \frac{(f + g) x}{(f - g) x}

f : (- \infty, \infty) \to (- \infty, \infty)

is defined by

f (x) = x (x - 1) (x - 2)

. Then

f

Join BYJU'S Learning Program

limitx→∞sinxx=

The correct option is C 0Explanation for the correct option:Evaluating the limitlimitx→∞sinxxwhen we substitute limit it becomes the value sin∞∞ where sin∞∈-1,1=-1,1∞=0×-1,1[∵1∞=0]=0Hence, option (C) is the correct answer

$l i m i t_{x \to \infty} \frac{\sin (x)}{x} =$