Question

lim (tan(x+h)−tan(x)h)
h->0​

Answer 1

lim (h_0) (1/h) (tan(x+h)- tanx)

=lim (h_0) (1/h) (sin(x+h) cosx-cos(x+h) sinx)/(cosx cos (x+h))

=lim(h_0) (1/h) (sin(x+h-x)/(cosxcos (x+h))

=lim(h_0) (sinh/h*lim(h_0) (cosxcos(x+h))

=1*1/(cosx*cosx)

=sec*2x

only 1mark u will write =sec*2x

And for 4 to 6 mark write full explanation

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