consider the following limit

Question

Consider the following limit.

 lim x→4 (7x + 4)

(a) Find the largest δ > 0 such that |f(x) − L| < 0.01 whenever 0 < |x − c| < δ.

 (Round your answer to five decimal places.)

δ = 

(b) Find the largest δ > 0 such that |f(x) − L| < 0.005 whenever 0 < |x − c| < δ.

 (Round your answer to five decimal places.)

δ = 

Answer 1

L = 7(4) + 4 = 32, c = 4, f(x) = 7x + 4

Let δ = 0.01/7 = 0.00143

If l x - 4 l < 0.01/7, then l 7x - 28 l = l (7x + 4) - 32 l < 0.01

So, if l x - c l < 0.01/7, then l f(x) - L l < 0.01

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Let δ = 0.005/7 and proceed as above.