Question

if f(x) = log/x-1 if x is not equal to 1 and k if x is equal to 1 continous at x= 1 then value of k is​

Answer 1

Step-by-step explanation:

Let f(x) = 5, , x * k, X = 0 if f(x) is continuous at x = 0, then k is equal to— T 5 (a) 5 ... x < 2, 2x – 1, when x = 2, then f" (2) is equal to— (a) 0 (b) 1 (c) 2 (d) does not 

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Answer 2

Given:

f(x) = log/x-1  ,    x ≠ 1

f(x) = k           ,    x = 1

To Find :

the value of k.

Solution:

We know  that f(x) is continuous at x = 1, so

k = $\lim_{x \to 1}\frac{logx}{x-1}$

As it is in $\frac{0}{0}$ form in the limit, According to the L-hospital rule

k = $\lim_{x \to \11} \frac{\frac{1}{x} }{1}$

  = 1

Hence, The value of k is 1.

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