# Math Help - limit + integral

1. ## limit + integral

Hey,
Any help would be appreciated.
I'm not even sure where to start.

Compute

lim (x^2)/x-3 [Integral] (from 3 to x) (sin t)/t dt
x->3

2. L'Hopital?

$\lim_{x \to 3} \frac{x^2 \cdot \frac{\sin{x}}{x} + 2x \cdot \int_3^x \frac{\sin{t}}{t}\,dt}{1}$

3. Power series allowed?

I haven't checked it well though.

4. Let $F(x) = \int_{3}^{x} \frac{\sin t}{t} \ dt$.

Note: $F(3) = 0$

So: $\lim_{x \to 3} \frac{x^2}{x-3} \cdot \int_{3}^{x} \frac{\sin t}{t} \ dt \ = \ \lim_{x \to 3} x^2 \cdot \frac{F(x) - F(3)}{x - 3} \ = \ \lim_{x \to 3} x^2 \ \cdot \ \underbrace{\lim_{x \to 3} \frac{F(x) - F(3)}{x - 3}}_{F'(3)} \ = \ \hdots$