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, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.