1ya correct
bt plz help me solve this both directly by derivative method/alhopitals/chain rule
also by 1st principle
the question is x2-√x/(√x)-x limit x tending to 1 plz solve this both by dirct derivative and 1st priciple 2)√tanx solve this by 1st principle
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10 Answers
1questn 1 isnt clear regarding wer the root stops...
can u plz insert (brackets)
62question 1 take √x=t
(t4-t)/(t-t2)
=t(t3-1)/(t(1-t))
Now you can take it from here..
162question 1 take √x=t
=t(t3-1)/(t(1-t))
=-(t2+t+1) = -3
what do you mean by direct derivative? (we need to find the limit!!)
62(√tanx+h-√tanx)
h
=
( tanx+h-tanx)
h(√tanx+h+√tanx)
now this is direct from expansion of tan x+h
62tanx(tanx-1)(tanx+1)
=tanx(sinx-cosx)(sinx+cosx)/cos2x
=√2tanx(1/√2sinx-1/√2cosx)(sinx+cosx)/cos2x
=√2tanx(sin(x-pi/4))(sinx+cosx)/cos2x
=-√2tanx(sin(pi/4-x))(sinx+cosx)/cos2x
=-√2tanx(cos(pi/4+x))(sinx+cosx)/cos2x
now the given question we have to divide by cos (pi/4+x)
so the given question becomes
=-√2tanx(sinx+cosx)/cos2x
=-√2√2/(1/2) = -4
62check for mistakes in the above..
I think it should be right though!