the limit represents the derivative of some function ( f ) at some number ( a ). state such an ( f ) and ( a…

the limit represents the derivative of some function ( f ) at some number ( a ). state such an ( f ) and ( a ).\n lim _{h \rightarrow 0} \frac{(1+h)^{4}-1}{h} \n( \bigcirc f(x)=x^{3}, a=2 )\n( \bigcirc f(x)=x^{4}-x, a=1 )\n( \bigcirc f(x)=x^{4}, a=1 )\n( \bigcirc f(x)=x^{4}+x, a=0 )\n( \bigcirc f(x)=x^{5}, a=0 )

the limit represents the derivative of some function ( f ) at some number ( a ). state such an ( f ) and ( a ).\n lim _{h \rightarrow 0} \frac{(1+h)^{4}-1}{h} \n( \bigcirc f(x)=x^{3}, a=2 )\n( \bigcirc f(x)=x^{4}-x, a=1 )\n( \bigcirc f(x)=x^{4}, a=1 )\n( \bigcirc f(x)=x^{4}+x, a=0 )\n( \bigcirc f(x)=x^{5}, a=0 )

Answer

Explanation:

Step1: Recall the definition of the derivative

The derivative of a function (f(x)) at (x = a) is given by (f^{\prime}(a)=\lim_{h\rightarrow0}\frac{f(a + h)-f(a)}{h}).

Step2: Compare with the given limit

Given (\lim_{h\rightarrow0}\frac{(1 + h)^{4}-1}{h}). If we set (f(x)=x^{4}) and (a = 1), then (f(a + h)=(1 + h)^{4}) and (f(a)=1^{4}=1).

Answer:

(f(x)=x^{4}), (a = 1) (the third option).