Differentiate the following by using "limit"
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Step-by-step explanation:

we want to differentiate the following by using limit:

derivative definition by limit given by

given that,

f(x)=√x

so,

f(x+∆x)=√(x+∆x)

thus substitute:

multiply both the numerator and denominator by the conjugate of the numerator:

simplify which yields:

simplify square:

collect like terms:

reduce fraction:

get rid of ∆x as we are approaching its to 0

simplify addition:

and we are done!

1. d.90

2. e. none of these (80)

3. a. 0

4. b. 6

5. e. none of these (10)

6. a. 5