Can you please help me with these? I got them wrong on a test and I don\'t under

Question

Can you please help me with these? I got them wrong on a test and I don't understand the correct answers. Thanks so much!

12. Let f(x) The graph off has which of the following lines as horizontal asymptotes? (A) y 3 only (B) y 3 and y 3 only (c) 1 only (D) y 3, y 3, y 1 and y -1 only 13. (Calculator) The height h, in meters, of a particle at time t is given by h(t) n 24t 24t3/2 16t What is the height of the object at the instant when it reaches its maximum upward velocity? (A) 2.545 meters (B) 10263 meters (C) 34.125 meters (D) 54,889 meters 14. (Calculator) The first derivative of the function f given by f (a) en-t is How many critical values does f have on the open interval (0,10)? (A) One (B) Three (C) Four (D) Five 15. Using the tangent line approximation for f(x) at a a 9, we have 2 (A) 3.133 (B) 2.866 (C) 2.863 (D) 2.733

Explanation / Answer

12)y =limx-> 3x/(x2-1)

y =limx-> 3x/|x|(1-(1/x))

y =limx-> 3x/(x)(1-(1/x))

y =limx-> 3/(1-(1/x))

y = 3/(1-0)

y=3

y =limx->- 3x/(x2-1)

y =limx->- 3x/|x|(1-(1/x))

y =limx->- 3x/(-x)(1-(1/x))

y =limx->- -3/(1-(1/x))

y = -3/(1-0)

y=-3

horizontal symptotes are y =-3 and y =3 only

13)h(t)=24t +24t3/2-16t2

velocity v(t)=dh/dt=24+36t1/2-32t

v'(t)=18t-1/2-32

for maximum upward velocity v'(t)=0

18t-1/2-32=0

t-1/2=32/18

t1/2=18/32

t=81/256

h(81/256)=24(81/256) +24(81/256)3/2-16(81/256)2

h(81/256)=10.263 meters

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