Question

If an equation of a tangent to the curve,y=cos(x+y),
-1<= x <= 1+ π is x+2y=k then k is equal to?

Answer 1

i differentiated the curve eq to get the tangent eq.

Answer 2

then i equated the slope to -1/2 (i found this thro' the tang. eq)

Answer 3

then find at what value of (x,y) you get slope= -1/2

Answer 4

i got x+y=π/2

Answer 5

after that how to find the value of x?

Answer 6

we need another eq for that...

Answer 7

should i substitute x=1+π or x=1?

Answer 8

*-1

Answer 9

\[y' = -\sin(x+y) (1+y')\]But you're given \(y' = -1/2\). So \(x+y = \pi/2\). Therefore, \(y = \cos(\pi/2) = 0\). We need the point where \(y = 0\) and \(x + y = \pi/2\) intersect. So the point is \((\pi/2, 0\). Now substitute to the equation of tangent and you get \(k = \pi/2\). I'm not sure if we have other solutions to this.

Answer 10

why y=cos(π/2)=?

Answer 11

y = cos(x+y) is your function

Answer 12

oh ya fine!

Answer 13

thank u