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  • Choose the correct answer out of 4 options given against each Question If f(x)=(x^n-a^n)/(x-a)for some constant ‘a’, then f’(a) is A. 1 B. 0 C. does not exist D. 1/2

Choose the correct answer out of 4 options given against each Question

If f \left( x \right) =\frac{x^{n}-a^{n}}{x-a}

for some constant ‘a’, then f’(a) is
A. 1
B. 0
C. does not exist
D.  1/2

Answers (1)

\\f \left( x \right) =\frac{x^{n}-a^{n}}{x-a} \\ \\ f^{'} \left( x \right) =\frac{ \left( x-a \right) \left( nx^{n-1} \right) - \left( x^{n}-a^{n} \right) \left( 1 \right) }{ \left( x-a \right) ^{2}} \\ \\ f^{'} \left( a \right) =\frac{ \left( a-a \right) \left( na^{n-1} \right) - \left( a^{n}-a^{n} \right) \left( 1 \right) }{ \left( a-a \right) ^{2}}=\frac{0}{0} \\ \\

Hence, the answer is option C

 

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infoexpert21

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