Question

find number of solutions of equation sinx=-4x +1

Answer 1

Answer:

Only one solution

x ≈ 0.2    ( x in radians)

x ≈ 0.2489 ( x in degress)

Step-by-step explanation:

find number of solutions of equation sinx=-4x +1

Sinx Range is -1 to 1

=>  -1 ≤ -4x +1 ≤ 1

Multiplying by -1

=> 1 ≥ 4x -1 ≥ -1

=> 1/2 ≥ x  ≥ 0

x lies between 0 & 1/2

1/2  radian  =  (1/2) π /(22/7)  = 7π/44 ° = 28.64°

Sinx > 0  & less than 1/2    ( as sin30° = 1/2)

Sinx is increasing with increasing x

and 1 - 4x is decreasing  with increasing x

0 < 1 -4x < 1/2  =>  1/4 > x > 1/8

so only one solution will exist  x ≈ 0.2  

If considering x into degrees only

then x lies between 0 & 1/2 degree

then Sinx lies between  0 & 0.01

0 < 1 -4x <  0.01

=> 0.25 > x > 0.2475

=> x ≈ 0.2489

Again only one solution