Question #a30c5
1 Answer
Aug 12, 2017
y=1
Explanation:
- Find the derivative of the function using the quotient rule:
#dy/dx = ((1+cosx)(cosx)-(sinx)(1-sinx))/(1+cosx)^2# - Find the instantaneous rate of change of the tangent line at the point
#pi/2# by plugging in#x=pi/2# and solving for#dy/dx# .
#dy/dx = m = ((1+0)(0)-(1)(1-1))/(1+0)^2 = 0# - Write the general equation for a line:
#y-y_1=m(x-x_1)# - Solve for y_1 by plugging in
#x=pi/2# into the original equation and solving for y
#y_1=sinx/(1+cosx)#
#y_1=1/(1+0)=1# - Solve for the equation of the tangent line with point
#(pi/2, 1)#
#y-1=0(x-(pi/2))#
#y=1#