# In the limit #lim 10x=40# as #x->4#, how do you find #delta>0# such that whenever #0<abs(x-4)<delta#, #abs(10x-40)<0.01#?

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To find the value of delta, we can start by manipulating the given expression abs(10x-40)<0.01.

First, we can simplify the expression by dividing both sides by 10, which gives us abs(x-4)<0.001.

Now, we need to find a value for delta such that whenever 0<abs(x-4)<delta, the inequality abs(x-4)<0.001 holds true.

Since the absolute value of a number is always positive, we can rewrite the inequality as -0.001<(x-4)<0.001.

To ensure this inequality holds true, we can set delta=0.001.

Therefore, whenever 0<abs(x-4)<0.001, the inequality abs(10x-40)<0.01 will be satisfied.

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