2. Evaluate the following limits: a) \( \lim _{x \rightarrow 0} \frac{x^{20}-20 x^{3}+3 x-7}{x^{15}+10 x^{8}-x^{6}+x-1} \lim _{x \rightarrow 0} \), b) \( \lim _{x \rightarrow \infty}\left(1-\frac{1}{3 x}\right)^{6 x} \) c) \( \lim _{x \rightarrow \infty}\left(\ln \left(x^{4}+x\right)-\ln \left(2 x^{4}-3\right)\right) \)

The following function is given. \[ f(x)=3 x^{3}-7 x^{2}-75 x+175 \]

\( \lim _ { h \rightarrow 0 } \frac { ( x + n ) ^ { 2 } - x ^ { 2 } } { h } \)

\[ f^{\prime \prime}(x)=\frac{4}{x^{3}} \] etudiar la concuvite

Evaluate the double integral \[ I=\iint_{A} 18 y e^{x^{2}} d x d y \] when \( A \) is the region in the first quadrant bounded by the graphs of \[ x=y^{2}, \quad x=2, \quad y=0 \] 1. \( I=18\left(e^{4}+1\right) \) 2. \( I=\frac{9}{2}\left(e^{4}-1\right) \) 3. \( I=9\left(e^{4}-1\right) \) 4. \( I=\frac{9}{2} e^{4} \) 5. \( I=\frac{9}{2}\left(e^{4}+1\right) \)

\( f(x)=\left(x^{2}+1\right)^{2} \) es