5. Particle \( X \) moves along the positive \( x \)-axis so that its position at time \( t \geq 0 \) is given by \( x(t)=5 t^{3}-9 t^{2}+7 \). (a) Is particle \( X \) moving toward the left or toward the right at time \( t=1 \) ? Give a reason for your answer. (b) At what time \( t \geq 0 \) is particle \( X \) farthest to the left? Justify your answer. (c) A second particle, \( Y \), moves along the positive \( y \)-axis so that its position at time \( t \) is given by \( y(t)=7 t+3 \). At any time \( t, t \geq 0 \), the origin and the positions of the particles \( X \) and \( Y \) are the vertices of a triangle in the first quadrant. Find the rate of change of the area of the triangle at time \( t=1 \). Show the work that leads to your answer.

\( \lim _ { x \rightarrow 0 } ( \frac { a - \cos ( \underline { 3 } x ) } { x - \sin ( b x ) } ) = ? \)

Use the given function to complete parts (a) through (e) below. \( f(x)=x^{4}-36 x^{2} \) A. \( x=\square \) (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There are no \( x \)-intercepts at which the graph touches the \( x \)-axis and turns around. c) Find the \( y \)-intercept by computing \( f(0) \). (0) \( =\square \) d) Determine the symmetry of the graph. Odd; origin symmetry

Use the given function to complete parts (a) through (e) below. \( f(x)=x^{4}-36 x^{2} \) c) Find the \( y \)-intercept by computing \( f(0) \). \( f(0)= \) d) Determine the symmetry of the graph. Odd; origin symmetry Even; \( y \)-axis symmetry Neither

Use an appropriate test to determine whether the following series converges. \( \sum_{\mathrm{k}=1}^{\infty} \frac{5}{\sqrt{\mathrm{k}^{3}}} \) Select the correct choice below and fill in the answer box to complete your choice. A. The series diverges. It is a p-series with \( \mathrm{p}=\square \). The series converges. It is a p-series with \( \mathrm{p}=\square \). C. The series diverges by the Integral Test. The value of \( \int_{1}^{\infty} \frac{5}{\sqrt{\mathrm{x}^{3}}} \mathrm{dx} \) is \( \square \). D. The series converges by the Divergence Test. The value of \( \lim _{\mathrm{k} \rightarrow \infty} \frac{5}{\sqrt{\mathrm{k}^{3}}} \) is \( \square \). E. The series diverges by the Divergence Test. The value of \( \lim _{\mathrm{k} \rightarrow \infty} \frac{5}{\sqrt{\mathrm{k}^{3}}} \) is \( \square \).

Math 60 Exam \#4 1) Use Right-endpoint Rule with \( n=5 \) to approximate \( \int_{2}^{3} x \sqrt{x+1} d x \) to 4 decimal places.