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  • Can someone explain - Limit , continuity and differentiability - JEE Main-18

If the function.

g(x)=   \left \{ \right. 

is differentiable, then the value of k + m is :

  • Option 1)

    2

  • Option 2)

    \frac{16}{5}

  • Option 3)

    \frac{10}{3}

  • Option 4)

    4

 

Answers (1)

best_answer

As we have learned

Continuity at a point -

A function f(x)  is said to be continuous at  x = a in its domain if 

1.  f(a) is defined  : at  x = a.

2. \lim_{x\rightarrow a}\:f(x)\:exists\:means\:limit\:x\rightarrow a

of  f(x) at  x = a exists from left and right.

3. \lim_{x\rightarrow a}\:f(x)=f(a)\:then\:the\:limit\:equals \:the\:value\:at\:x=a

-

 

 

Condition for differentiability -

A function  f(x) is said to be differentiable at  x=x_{\circ }  if   Rf'(x_{\circ })\:\:and\:\:Lf'(x_{\circ })   both exist and are equal otherwise non differentiable

-

 

 FOr continuity at x= 3 , 

 k \times 2 = = 3m+2 .........(1)

and for diffrentiability at x = 3 , 

 \frac{k}{2\sqrt{x+1}}|_{x=3}= m

 

\Rightarrow K = 4m .......(2)

solving (1) and (2) 

m = 2/5 

and k = 8/5 

therfore m+k = 2 

  

 

 

 

 

 


Option 1)

2

Option 2)

\frac{16}{5}

Option 3)

\frac{10}{3}

Option 4)

4

Posted by

Himanshu

View full answer

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