-- S P₂ (t) dt 0 P₁(x) = 1 P₂(x) = cos x 1 + ¹+ ſ P3 (t) dt X P3(x) = cos x + 9₁ (t) dt 0

Q: Find f. f"(x) = cos(x), f(0) = 3, f'(0) = 6, f"(0) = 4

A:

Q: Suppose h(x) = cos(tť² )dt Calculate h' (x).

A: Given: hx=∫0x3cosπt2dt.

Q: Find f. f'(t) 8 cos(t) + sec?(t), -7/2 <t < a/2, f(a/3) = 5 f(t) =

A: Given

Q: xpress tiIE SS the f (x) = 3 sin? x + cos? x of oog m

A:

Q: Find f. f"(x) = cos(x), f(0) = 6, f'(0) = 4, f"(0) = 9 f(x) =

A: We can find the value of f(x) as below.

Q: Find f. a) f '''(x) = cos(x),    f(0) = 7,    f '(0) = 8,    f ''(0) = 8   b) A particle is moving…

A:

Q: Find f. f "(x) = 7 + cos(x), f(0) = -1, f(71/2) = 0 %3D %3D

A:

Q: find /x – x² - dx xV4x – x² dx 9. 10. х dx dx 11. 12. xV7 – x² xV7 + x² Vx² (4 x² 4 dx 13. 14. х sin…

A:

Q: G(x) = cos osV5t) dt G'(x) =

A: Recall: Leibnitz Integral Rule:              ∂∂x∫a(x)b(x)f(x,t) dt=∫a(x)b(x)∂f(x,z)∂xdt…

Q: Find f. f '(t) = 2 cos(t) + sec2(t),    −π/2 < t < π/2,    f(π/3) = 4

A:

Q: The function f(x) = a sin x + b cos x + c satisfies f"(x) = cos x – 2 sin x, f'(0) = f(0) = 2. Find…

A: a=2 b=-1 c=3

Q: Compute the derivative of f(x) = ( sin(2x + 1))/°. 4 (sin(2x+ 3 1) -1/3 • cos (2x + 1) 4 -1/3…

A: Given

Q: Find f. f(x) = f"(x) = cos(x), f(0) = 9, f'(0): = = 8, f "(0) = 6

A: Given,  f'''(x)=cosx, f(0)=9, f'(0)=8, f''(0)=6

Q: Find f. f"(x) = 5 + cos(x), f(0) = -1, f(9π/2) = 0

A:

Q: Determine which of the following pairs of functions are linearly independent. NO ANSWER + 1. f(x) =…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A power signal which is periodic with period 2n and is characterized by the form f(x) Expand f(x) in…

A: Given, fx=sinhxcosx, -π≤x≤π Since, f is periodic of period 2π then, fx+2π=fx Then,…

Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx b.…

A: Separable equation:   A first order differential equation y’ = f (x, y) is called a separable…

Q: Find f if f"(x) = 2 + cos(x), f(0) = -9, f(pi/2)=9 f(x) =

A: Solution of given question is followed by:

Q: Find f. f(t) = f'(t) sec(t) (sec(t) + tan(t)), -2-√2 x Need Help? Read It Watch It - 1/2 < t < 1/₁ (…

A:

Q: a fif f" (t) = 2e* +3 sin(t), f(0) =-8, ) =

A:

Q: 8e cos 2x dx csc(x) sec(x)

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Q: dF Find dx or F(x) COS x 1-) F(x) = S* /1 + t³ dt sin x

A:

Q: Find f. f "(x) = 5 + cos(x), f(0) = –1, f(9/2) = 0 f(x) : %D

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Q: x² + 2x – 3 dx 2x + |x – 3| 1. 6 sec 2t + tan 2t dt 2. Cos 2t kloc

A:

Q: Q1) find dy/dx 1) F(x) = sin’2x tan x² x – 3 ) 2) F(x) = sin( x +4

A:

Q: COs ax dx. x² + b² (q)

A: Cauchy residue theorem: If f is holomorphic function defined on simply connected open set with…

Q: Find f if f"(x) =2 + cos(x), f(0) = 10, f(t/2) = -5. f(x) = |

A: To find f if f"x=2+cosx, f0=10, fπ2=-5. Solution: We have, f"x=2+cosx Integrating both sides, we get…

Q: Find f if f"(x) = 2 + cos(x), f(0) = -10, f(x/2) = 4. %D %3D f(x) = iii

A: Recall: ∫xn dx= xn+1n+1+c; where c is an integration constant. ∫sinx dx= - cos(x)+c; where c is an…

Q: Find f. f"(8) = sin(e) + cos(e), f(0) = 5, f'(0) = 4 f(e) = 5t – sin (t) – cos(t) + 6

A: Here we have f''θ=sinθ+cosθ, f(0)=5, f'(0) = 4 fθ=?

Q: Differentiate the functions. a) f(x) = 2 – 5x + b) f(x) = e* + cosx c) f(x) = d) f(x) = (5 – x²)· e*

A: Suppose f and g are differentiable function .Then note the following results : The power rule of…

Q: solve  sin(x)dy/dx + ycos(x) = cos(x)[ex + sec2(x)].

A: Convert into dy/dx+p(x) y=Q(x)