If the function f(x)=3x−8, if x≤52k, if x>5 is continuous, then the value of k is:

Given: f(x)=3x−8, if x≤52k, if x>5As f is continuous, so it will be continuous at 5. ⇒limx→5- f(x)=limx→5+ f(x)⇒limx→5 (3x−8)=limx→5 2k⇒15−8=2k⇒k=72

If the function f(x)=3x−8, if x≤52k, if x>5 is continuous, then the value of k is:

Given: f(x)=3x−8, if x≤52k, if x>5As f is continuous, so it will be continuous at 5. ⇒limx→5- f(x)=limx→5+ f(x)⇒limx→5 (3x−8)=limx→5 2k⇒15−8=2k⇒k=72

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If the function $f (x) = \{\begin{matrix} 3 x - 8, if x \leq 5 \\ 2 k, if x > 5 \end{matrix}$ is continuous, then the value of k is:

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$\frac{2}{7}$

$\frac{7}{2}$

$\frac{3}{7}$

$\frac{4}{7}$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given: $f (x) = \{\begin{cases} 3 x - 8, if x \leq 5 \\ 2 k, if x > 5 \end{cases}$
As f is continuous, so it will be continuous at 5.
$\begin{array}{l} \Rightarrow lim_{x \to 5^{-}} f (x) = lim_{x \to 5^{+}} f (x) \\ \Rightarrow lim_{x \to 5} (3 x - 8) = lim_{x \to 5} 2 k \\ \Rightarrow 15 - 8 = 2 k \\ \Rightarrow k = \frac{7}{2} \end{array}$