If left begin matrix fracx - 2-x2 x- x neq 0 k - x -0lend matrix -right and if f is continuous at x -0-then k - -A- 0 B- 1D- 1-2D- -1-2

The correct option is D Given function, f(x) = {x^2 x/2x, x ≠ 0 k, x = 0 . Since its given taht f(x) is continuous, lim_x→ 0f(x)=f(0) i.e., lim_x→ 0x^2 x/2x= ...

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

Byju's Answer

Standard XII

Mathematics

Rate of Change

If left begin...

Question

If ${\begin{matrix} \frac{x^{2} - x}{2 x}, x \neq 0 k, x = 0 \end{matrix}$ and if f is continuous at x=0,then k=?

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

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

Open in App

Solution

The correct option is D

Given function,

f(x) = ${\begin{matrix} \frac{x^{2} - x}{2 x}, x \neq 0 k, x = 0 \end{matrix}$

Since its given taht f(x) is continuous,

$lim x \to 0 f (x) = f (0)$

i.e., $lim x \to 0 \frac{x^{2} - x}{2 x} = k$

$lim x \to 0 \frac{x - 1}{2} = k \Rightarrow k = - \frac{1}{2}$

Suggest Corrections

Similar questions

Q. If

f (x)

is continuous at

f (x) = \begin{matrix} \frac{1 - cos k x}{x^{2}}, = \frac{1}{2}, \end{matrix} \begin{matrix} f o r x \neq 0 f o r x = 0 \end{matrix}

Find

k

Q. If

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \frac{1 - cos x}{\begin{matrix} x k \end{matrix}} \begin{matrix} x \neq 0 x = 0 \end{matrix} ⎫ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎭

is continuous at

x = 0

, then the value of

k

is:

$f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 2^{x + 2} - 16 & i f x \neq 2 \begin{matrix} 4^{x} - 16 k \end{matrix} & i f x = 2 \end{matrix} a t x = 2$

If f(x) is continuous at x=2, then find the value of k.

Q. If

f (x) = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{sin 5 x}{x^{2} + 2 x}, & x \neq 0 k + \frac{1}{2}, & x = 0 \end{matrix}

is continuous at

x = 0

, then the value of

k

Q. If

f (x) = {\begin{matrix} x^{a} cos (1 / x), & i f & x \neq 0 0, & i f & x = 0 \end{matrix}

is continuous at

x = 0

then

Join BYJU'S Learning Program

If {x2−x2x,x≠0k,x=0 and if f is continuous at x=0,then k=?

The correct option is D Given function, f(x) = {x2−x2x,x≠0k,x=0 Since its given taht f(x) is continuous, limx→0f(x)=f(0) i.e., limx→0x2−x2x=k limx→0x−12=k⇒k=−12

If ${\begin{matrix} \frac{x^{2} - x}{2 x}, x \neq 0 k, x = 0 \end{matrix}$ and if f is continuous at x=0,then k=?