sinon fex) = Find a fonction fix such that f'(x) = -4e²+ x and f(0) =2 11A 159 26d 1916 126 k

Q: Find the derivative of fl6)-32" ). (v²+5) tan (5x

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Q: The population in millions of arctic founder in the Atlantic ocean is modeled by the function P (t)…

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Q: Use function f Gx)= X-cos(x) to %3D differedtinte Newton's fined Poird method and methed.

A: Given that f(x)=x-cosx The newton method is, xn+1=xn-f(xn)f'(xn) Then f'(xn)=1+sin x So, the…

Q: (D²+1)y = Y = seC X CSCX

A: The given differential equation is      (D2+1)y=secxcscx the complimentary solution for the given…

Q: prove the following relationships. Note that x(z) = ] [x(+)]. 1. ] [ a^² XLE)] = x ( ² / ) 2. ] […

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Q: Let f (t) = et sin 8t Part (a) Find L{f(t)}

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Q: A formuia for a function y = f(x) is f(x) = 5x° Find f '(x) and identify the domain and range of f…

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Q: Use the rule for square roots: f'(x) 2/ F(x) V F(x) to find the following derivatives (quickly d V…

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Q: Find of the fo lloming function the derivative Tin C A y'= (Sinsc) oc Sin 6-1 Sinac +Inx cos scl +…

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Q: FIHD THE DERIVATIVE OF THE GIVEM. FUMCTION Cos? x 1-) g(x) = 2)f(x)= Sinメ tany Sinx tan y sec x Cot…

A: topic - derivatives

Q: Let f (t) = e5t sin 4t Part (a) Find L{f (t)} Part (b) Find L{f' (t)}

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Q: ) FIND F'6): c. f() - x 2- 3x2 F. f6) = VI-x

A: f(x)=x2-3x2differentiate w.r.t.…

Q: Q1) Evaluate: (a) fe²_1_dx Inx sin ¹x 1-x² dx (b) f 1- cos dx (e) Jỗ 2sinx cosx dx (c) | Inx dx

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Q: Q2\Find T.E of the function f (x) = sin 2x when a =1?

A: Given that  f(x)=sin(2x) at a=1  To find the T.E

Q: 2t Show that f/² sin tdt ≥ 7. (Hint: sin t ≥ ㅠ over [0, 1].)

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Q: Use L and L to solue y' t 3y= f4) y)=5, where f4), (32)

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Q: Q5) consider the function f(x)= cos x-x30. Approximate a root of using Newton method .let xo= /4

A: Given function, fx=cosx-x To find the approximate root of the function using Newton's method.

Q: Use function f(x)=x-Cos(x) to differentiate Newton,s. Method and Fixed point method. Explain it…

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Q: Suppose the velocity of a ninja is given by v = ft, 3t², sin(π) at time t. If the position of the…

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Q: Q3 A) Sketch the function y=sech' x , then write the properties of this function. 30 B) Evaluate Two…

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Q: (x² +8) cotx 2 - cos x csc x Find f' (x) when f (x) = 2x cot x – (x² + 8) csc²x A. f' (x) = csc²x 4x…

A: As we know that; The Quotient rule: fg'=f'·g-g'·fg2 The Product rule: f·g'=f'·g+f·g' The…

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Q: b.9f Fex)=x Sin lgix), where gL1)= , and g' (1)= -1, then f'(1)=2

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Q: sin (), x + 0 10. Find the value of K which makes f (x) K, x = 0 continues at x = 0.

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Q: Prove dx dx 1 f ( sec -x+tan –I 2 1 | f (cosecz) %3D Vsin r sin x

A: Apply trigonometric properties to prove the result.

Q: Q12. If fla)= tann- 3 secu find f'(a) = find f'E) =

A: first derivative of f(x) is f'(x)= cos x+3sinx