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Given that the derivative f'(a) exists. ...

Given that the derivative `f'(a)` exists. Indicate which of the following statements(s) is/are always true?
a. `f'(a)=lim_(htoa)(f(h)-f(a))/(h-a)`
b. `f'(a)=lim_(hto0)(f(a)-f(a-h))/h`
c. `f'(a)=lim_(t to0)(f(a+2t)-f(a))/t`
d. `f'(a)=lim_(t to0)(f(a+2t)-t(a+t))/(2t)`

A

`f'(a)=lim_(htoa)(f(h)-f(a))/(h-a)`

B

`f'(a)=lim_(hto0)(f(a)-f(a-h))/h`

C

`f'(a)=lim_(t to0)(f(a+2t)-f(a))/t`

D

`f'(a)=lim_(t to0)(f(a+2t)-t(a+t))/(2t)`

Text Solution

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The correct Answer is:
A, C, D
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