3. Considere la siguiente función \[ f(x)=\left\{\begin{array}{ll}x^{2} \operatorname{sen}\left(\frac{1}{x}\right) & \text { si } x \neq 0 \\ 0 & \text { si } x=0\end{array}\right. \] Demuestre que existe \( c \in(-\pi, \pi) \) tal que \( f(c)=1 \) Pista: Para mostrar la continuidad en \( x=0 \), use que \( \left|\operatorname{sen}\left(\frac{1}{x}\right)\right| \leq 1 \)

Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. \( \int \frac{x^{2} d x}{\sqrt{25+x^{6}}} \) \( \int \frac{x^{2} d x}{\sqrt{25+x^{6}}}=\square \)

Question \( \triangle M T K \) can be mapped onto \( \triangle V D Q \) by a reflection. If \( \mathrm{m} \angle M=65^{\circ} \), find \( \mathrm{m} \angle V \). Answer Attempt 1 out of 4 \( \mathrm{~m} \angle V \quad \) watch Video Solamples \( \triangle \) be determined.

C. Solve the following problems. 11. Find the simple interest on a loan of \( P 65,000 \) if the loan is given at a rate of \( 20 \% \) and is due in 3 years.

5. Bentuk sederhana dari \( \left(\frac{b^{-1} a}{a^{-2} b}\right)^{3}= \) A. \( \frac{a^{12}}{b^{9}} \) B. \( \frac{a^{9}}{b^{6}} \) C. \( \frac{a^{6}}{b^{3}} \) D. \( \frac{a^{3}}{b} \)

3. What is the maximum value of the function \( f(x)=-2 x^{2}-3 x+4 \) ? (A) 5.13 (B) 3.38 (C) 2.25 (D) 1.13 (E) 0.56