Answer:

here some

function f is given by the limit

Substitute by in the above definition to obtain

The above limit is of the indeterminate form . Multiply the numerator and denominator by the conjugate of the numerator

Expand the numerator and simplify

Divide numerator and denominator by (or cancel )

Evaluate the limit and hence the derivative

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Answer:

The derivative of function f at x=c is the limit of the slope of the secant line from x=c to x=c+h as h approaches 0. Symbolically, this is the limit of [f(c)-f(c+h)]/h as h→0.

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