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Differentiate the function. 4 Y = 28 +Differentiate. sec(8) tan(8) XA graphing calculator is recommended. A particle moves according to a law of motion s = A(t), t 2 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = sin at (a) Find the velocity (in ft/s) at time t. v(t) = ft/s (b) What is the velocity (in ft/s) after 1 second? V(1) = ft/s (c) When is the particle at rest? (Use the parameter n as necessary to represent any integer.) (d) When is the particle moving in the positive direction for 0 s t s 6? (Enter your answer using interval notation.) (e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds. ft (f) Find the acceleration (in ft/s ) at time t. a(t) = ft/s2 Find the acceleration (in ft/s ) after 1 second. =(1) = ft/=2(g) Graph the position, velocity, and acceleration functions for 0 s t = 6. -1 -2 -3 (h) When is the particle speeding up? (Enter your answer using interval notation.) When is it slowing down? (Enter your answer using interval notation.)Find the linear approximation of the function g(x) = V1 + x at a = 0. g(x)= V0.95 = Use it to approximate the numbers V 0.95 and V 1.1. (Round your answers to three decimal places.) V1.1=[ Illustrate by graphing g and the tangent line. 2 -4 -2 2 -2 -2 O -4 O -41 2 2 -2 LX 2 -2 0 2 -2 -2 O O -41Use differentials to estimate the amount of paint needed to apply a coat of paint 0.04 cm thick to a hemispherical dome with diameter 60 m. (Round your answer to two decimal places.) m 3