Hello, I need help with my calculus assignment, thank you, take your time. some questions may be select all that apply so make sure to select more than one answer.

An object moves along a straight line with position at time t given by s (t) = 3t4 cost . What is the velocity of the object at time t ? O v (t) = 12t3 cost + 3t* sint O v (t) = 12t3 sint O v(t) = -12+3 sint Ov (t) = 12+3 cos t - 3t sin tUse the information given in the table to nd the following derivatives. All answers are integers. a} If RG12) : (tam) Hm) then R' (i) b) If h(:1:) 2 it\"): then h" (71') = c) If L (3:) 2 PM then Km) = 00523 Suppose L is the tangent line of y = 3 tan x - 2 cscx atx = Where does L intersect the x-axis? O At x = 40 O At x = T V3 8 O At x = 3V/3 O At * = 3 09 4 8 O At * = 40T 3A student hands in the following work: Problem: Given that F (21:) : cos(si11w) nd F\" ( your answer to 3 decimal places. g) . Round Student answer: Line 1: The variable here is w , but the method used to differentiate is the same as if the variable had been :1: . Line 2: Recall that the derivative of y = COS a: is yr 2 Sins: and the derivative of y = 8111.1: is y' = cos :1: . Line 3: Using the Product Rule, we get: Line 4: Fr (10) = sin(sin w) + (305(003 00) Line 5: To find Fr (E) we need to evaluate Fr (10) at w = g . Line 6:131?) : 31143111?) + (305(003 %) ' . r 1 : _ ' 1 ; Line7.F (4) Sl('/)+COS(\\/) Line 8: Using a calculator to evaluate this, we get: Line 9: F' (g) m 0.6496369391 + 07602445971 Line 10: F' (g) m 0.650 + 0.760 = 0.110 Line 11: So the nal answer(to 3 decimal places) is 0.110I Is the student's work correct? {Write "yes" or "no".) If incorrect, in what line is the FIRST error? {Write 1, 2, or 11. If the solution is correct, write "none". Which of the following functions could be evaluated without using the Chain Rule? Select all that apply. O T(v) = (30 +7)2 O z = vsint O A (x) = tan (3ac2) OS(x) = 3 tan x Of (x) = tan(cos ac) O y = tan x cos xConsider f (a) = sin (5ac2 - ac) . Use the Chain Rule to find f' (a) . O f' (x) = cos (5x2 - x) (10x - 1) Of' (x) = cos(10x - 1) . 10 Of' (x) = cos(10x - 1) (10x - 1) Of' (x) = cos (5x2 - ac) . 10x Of' (x) = cos(10x - 1) Of' (x) = cos (5x2 - x) . 10x - 1Use the information in the table to find the derivatives. 1 2 3 TT 6 f (z) 3 6 10 f' (2) 2 0 9 2 5 f" (ze) 2 12 .8 4 V2 All final answers are integers. a) If h (a) = f (3ac) then h' (2) = b) If y = f (x2 + 2) then y' |x-1= c) If G (ac) = cos(f (a) ) then G' (TT) =A group of biologists have measured the lengths of a certain type of snake and model the average length (in centimeters) of the snakes at t weeks after birth to be: L (t) : 19 (1 (1 + 0.553t + 0.014t2)_1) What is the growth rate of an average snake, 3 weeks after birth? Round your nal answer to 2 decimal places