evalute the following limits
vii)
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so u wanted the other method....
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lim h->0 √(x+h) - √(x) / h. ........(1)
we know that
d[f(x)]/dx = lim h->0 f(x+h) - f(x) / h. .....(2)
in comparing eqn (1) & (2)
we have
f(x) = √(x)
f(x) = (x)^(1/2)
d[f(x)]/dx = d(x^1/2)/dx
= 1/2*x^(1-1/2) d(x)/dx
= 1/2x^-1/2
so
the answer is
1/2√(x)
:-)
we know that
d[f(x)]/dx = lim h->0 f(x+h) - f(x) / h. .....(2)
in comparing eqn (1) & (2)
we have
f(x) = √(x)
f(x) = (x)^(1/2)
d[f(x)]/dx = d(x^1/2)/dx
= 1/2*x^(1-1/2) d(x)/dx
= 1/2x^-1/2
so
the answer is
1/2√(x)
:-)
wc
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