limits of a function

Question

lim f(2+h) - f(2) / h

h-> 0

f(x) = X^2 - 2

Answer 1

 

lim f(2+h) - f(2) / h
h-> 0
f(x) = X^2 - 2
f(2)=4-2
f(2)=2
(f(2+h)-2)/h
(2-2)=0
limit value is 0

Answer 2

 

lim ((2x^2+5)/(2x^2+8))^(4x^2+5x+7) as x->+infinity

 

lim (sin^3(2*tan(x^2)))/(((1+(3*arctan 2x)-1)^1/3)^6) as x->0

 

lim ((3x-1)^2)((2x^2+5x-4)^3)/((x^5)((81x^12+64x^8+258)^1/4)) as x->infinity