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# limit of integral help. apparently the h in the 2+h does not make any difference. explanations would be appreciated?

### 4 Answers

- MorningfoxLv 73 years agoFavorite Answer
That expression as actually given does not have "x" in the integral. Is the upper limit perhaps supposed to be 2 + x? I will assume that is the correction to the typo. Then we have a thin slice of the function, from t = 2 to t = 2 + dx. So the integral is just the function sqrt( 1 + t^3), evaluated at t = 2, times dx. In other words, integral = 3dx. As dx --> 0, the integral --> 0.

If the correction to the typo is something else, then we might have to actually find the integral. It's a monster, with an elliptic integral and inverse sine.

- ted sLv 73 years ago
Hmmmm: will assume h ≡ x then the integral is G(x + 2) - G(2) where G ' exists ====> G is continuous ====>

answer is 0 as x ---> 0

- PopeLv 73 years ago
The limit has x approaching zero, but there is no x in the integral expression. The limit is simply the definite integral evaluated, and yes, of course the h makes a difference.

- JLv 73 years ago
I suspect a typo. The integral does not have any x. So the limit as x tends to zero is just the definite integral. It is a complicated function of h.