Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Help me understand! - Limit , continuity and differentiability - JEE Main-4

Letf\left ( a \right )= g\left ( a \right )= k and there n^{th} derivatives

f^{n}\left ( a \right ),g^{n}\left ( a \right ) exist and are not equal for some n. Further if

\lim_{x\rightarrow a}\frac{f\left ( a \right )g\left ( x \right )-f\left ( a \right )-g\left ( a \right )f\left ( x \right )+g\left ( a \right )}{g\left ( x \right )-f\left ( x \right )}= 4

then the value k is

  • Option 1)

    2

  • Option 2)

    1

  • Option 3)

    0

  • Option 4)

    4

 

Answers (1)

best_answer

As we learnt

L - Hospital Rule -

In \:the\:form\:of\:\:\;\frac{0}{0}\:\:and\:\:\frac{\infty }{\infty }\:\:\:we\:differentiate\:\:\frac{N^{r}}{D^{r}}\:\:separately.


\Rightarrow \lim_{x\rightarrow a}\:\:\frac{f(x)}{g(x)}=\lim_{x\rightarrow a}\:\:\frac{f'(x)}{g'(x)}

- wherein

\lim_{x\rightarrow a}\:\:\frac{\frac{d}{dx}\:f(x)}{\frac{d}{dx}\:g(x)}


Where \:\:f(x)\:\:and\:\:g(x)=0

 

 \lim_{x\rightarrow a} \frac{f\left ( a \right )g\left ( x \right )-f\left ( a \right )-g\left ( a \right )f\left ( x \right )+g\left ( a \right )}{g\left ( x \right )-f\left ( x \right )}=4

\lim_{x\rightarrow a} \frac{f\left ( a \right )g'\left ( a \right )-0-g\left ( a \right )f'\left ( x \right )+0}{g'\left ( x \right )-f'\left ( x \right )}=4

\frac{f\left ( a \right )g'\left ( a \right )-g\left ( a \right )f'\left ( a \right )}{g'\left ( a \right )-f'\left ( a \right )}=4

\frac{k\times g'\left ( a \right )-kf'\left ( a \right )}{g'\left ( a \right )-f'\left ( a \right )}=4

k\left [ \frac{g'\left ( a \right )-f'\left ( a \right )}{g'\left ( a \right )-f'\left ( a \right )} \right ]=4

\therefore k=4


Option 1)

2

Incorrect

Option 2)

1

Incorrect

Option 3)

0

Incorrect

Option 4)

4

Correct

Posted by

divya.saini

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’
anam-khan

NIT Puducherry Cut-off 2024: Computer Science and Engineering had highest closing rank last year
anam-khan

What after JEE Main results 2024? All you need to know about JEE Adv, CSAB, JoSAA counselling

Latest Question