What is the limit of this function as h approaches 0? #(h)/(sqrt(4+h)-2)#

Question

is this zero or undefined?

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Answer 1 · 2018-06-02T05:27:19

#Lt_(h->o)(h)/(sqrt(4+h)-2)#

#=Lt_(h->o)(h(sqrt(4+h)+2))/((sqrt(4+h)-2)(sqrt(4+h)+2)#

#=Lt_(h->o)(h(sqrt(4+h)+2))/(4+h-4)#

#=Lt_(h->o)(cancelh(sqrt(4+h)+2))/cancelh " as "h!=0#

#=(sqrt(4+0)+2)=2+2=4#

Answer 2 · 2018-06-06T14:32:45

# 4#.

Recall that, #lim_(h to 0)(f(a+h)-f(a))/h=f'(a)............(ast)#.

Let, #f(x)=sqrtx," so that, "f'(x)=1/(2sqrtx)#.

#:. f'(4)=1/(2sqrt4)=1/4#.

But, # f'(4)=lim_(h to 0)(sqrt(4+h)-sqrt4)/h............[because, (ast)]#.

#:. lim_(h to 0)(sqrt(4+h)-sqrt4)/h=1/4#.

#:." The Reqd. Lim."=1/(1/4)=4#.

Enjoy Maths.!