Please answer question 6 in its entirely, thanks! 6. A mass attached to a spring moves horizontally on a smooth surface. The position of the spring (in cm) in terms of thetime (in sec) is given by s(t) = 8 sin(t).a) Find expressions for the velocity and for the acceleration of the mass at time tITb) What are the position, velocity, and acceleration of the mass at t = =sec. and at t = sec? Is the mass moving offorward or backward? Is it going faster or slowing down?4c) When does the mass stop?8 cm8 cmb) v(t) = 8 cos(t), a(t) = -8 sin(t); c) s() = cm, v) = a() = -2, moving forward, slowing down and S(7) = 0.пv(n) = -8 a(n) = Omoving backward and constant velocity; d) t = = 3.... sec (approximately 1.5 sec, 4.7 sec, 7.8 sec, ...)mul oilodisg7. Find the indicated limits, use +∞ or -∞ when appropriate. Use L'Hospital's rule when needed (be sure to justifywhy you can use it)x-4a) lim.x-4x²-166x²-10x - 3x²+4xg) lima) 1/8b) 3√2b) limt→h)limx03cos tcos x-1c) 16/5c) limx→5d)i) limx-03x²-14x-5x2−5xsin 4xXsin xx→∞ exj) limd) limx0g) 2; h) 0; i) 43x²-14x-5x2-5xj) 0Inxe) limx+0+ ex-15√√x-1k) limx--∞ 10x²-xk) 0 1) 0InxX→∞ X1) limm) ∞f) lim tanhxx→→∞m) lime ¹/xx→0+8. Use the strategy discussed in class (first and second derivative tests, critical points, concavity, x- and y-intercepts,asymptotes, etc.) to analyze each given function and sketch its graph. Label all critical and inflection points

Name: Please answer question 6 in its entirely, thanks! 6. A mass attached t
Uploaded: 2024-03-05T11:56:34.000Z
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Description: Please answer question 6 in its entirely, thanks! 6. A mass attached to a spring moves horizontally on a smooth surface. The position of the spring (in cm) in terms of thetime (in sec) is given by s(t) = 8 sin(t).a) Find expressions for the velocity