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if f ‘(x) = a sin x + b cos x and f ‘(0) = 4 , f(0) = 3 , f(pi/2) =5 find f(x)

if f ‘(x) = a sin x + b cos x and f ‘(0) = 4 , f(0) = 3 , f(pi/2) =5 find f(x)

Grade:12

2 Answers

Arun
25750 Points
3 years ago
Dear student
 
f'(0) = 4 = b
f(x) = - a cos x + b sinx + c
Now
f(0) = 3 = -a + c
f(π/2) = 5 = b + c
Hence c = 1
And  a = -2
 
Hence f(x) =  2 cos x + 4 sin x +1
Vikas TU
14149 Points
3 years ago
Dear student 
Please refer the study material and example
Good Luck 

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