1- Use the function defined below to find an equation of the tangent line at the

Question

1- Use the function defined below to find an equation of the tangent line at the point indicated. y = sin(x), x = ?/3 ????????????????? 2- Use the Product and Quotient Rules as necessary to find the derivative of the given function. (Type theta for ?.) g(?) = 3e?/cos(?) ????????????????? 3- Use the Product and Quotient Rules as necessary to find the derivative of the given function. R(y)= cos(y)-1/sec(y) ???????????????? 4- Calculate the second derivative of the given function. f (x) = 5cot(x) ?????????????????????? 5- Find an equation of the tangent line at x = 0 for the given function. y = 5*e^x*cos(x) ???????????????????? 6- The height at time t (s) of a weight, oscillating up and down at the end of a spring is given below. s(t) = 700 + 80sin(t) (a) Find the velocity at t = ?/4 s. ??????????? cm/sec (b) Find the acceleration at t = ?/4 s. ??????????? cm/sec2

Explanation / Answer

1- Use the function defined below to find an equation of the tangent line at the point indicated. y = sin(x), x = ?/3 ?????????????????

y= sinx

x= pi/3

y = sin(pi/3) = sqrt(3) /2

slope = y' = dy/dx = cosx

slope = cos(pi/3) = 1/2

y - sqrt(3)/2 = 1/2( x - pi/3)

y = x + sqrt(3) - pi/3

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