# In the limit #lim_(t to oo) 1/(1+4t)=0# , how do you find #B>0# such that whenever #t>B#, #1/(1+4t)<0.01#?

Just solve the inequality

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To find B>0 such that whenever t>B, 1/(1+4t)<0.01, we can set up an inequality and solve for B.

Starting with the given limit, lim_(t to oo) 1/(1+4t)=0, we can rewrite it as 1/(1+4t) - 0 < ε, where ε is a positive number (in this case, ε=0.01).

Now, we can solve the inequality 1/(1+4t) < ε, which is equivalent to 1/(1+4t) < 0.01.

Multiplying both sides by (1+4t), we get 1 < 0.01(1+4t).

Expanding the right side, we have 1 < 0.01 + 0.04t.

Subtracting 0.01 from both sides, we obtain 0.99 < 0.04t.

Dividing both sides by 0.04, we get 24.75 < t.

Therefore, B>0 can be chosen as B=24.75, and whenever t>B, 1/(1+4t)<0.01.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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