I need thorough explanation, step by step, showing how to solve limit problems.

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1. lim ( ( √5x-4 ) -1) / 3x^2

x=>8

2. lim 2x-10/x^2-25

x=>5

3. Use the limit definition of the derivative to show that if: f(x)=mx+b, then f'(x)=m

4) Use limits to compute the derivative: f'(2), where f(x)=x^3

5) Apply the 3-step method to compute f'(x) for the function; simplify the difference quotient as much as possible before taking limits.

f(x)= -3x^2+1

6) The following limit is a definition of f'(a). Determine the function f(x) and the value of a.

lim ( (2+h)^3 -8 ) / h

h=>0

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