-T < x <0 f(x) = & f(r + 27) = f(x) | sin x 0

Q: The maximum value of F in F(x) = - 4 cos x is 2 4 1

A: We know range of cosine function is [-1,1] Therefore maximum value of f(x)= -4cosx is, f(x)=-4cosx…

Q: The trigonometric substitution x - 2 = 3 sec could be useful in integrating a function (i.e., an…

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Q: tan (3r) dr = a tan(3x) – In(v1 + 9x²) +C 3 a tan (3x) + In(v1+9r²) 3. e tan '(3x) In(v1 - 9x² +C a…

A: We know that, from basic integral formula ∫tan-1x=xtan-1x-12log1+x2+C          ⋯⋯1 We have, the…

Q: Find the sine transform of a function of x which is equal to sin x for 0 <x<a and 0 for x2a.

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Q: dx For - = In[F(x)]+C• What is f(/3) if C = 0? (x+x³) (x Tan-'x + 1) -1 - 6. + -1 - -15 -is -is

A: Integrate ∫dx(x+x3)(xtan-1x+1)

Q: 2*csch( 2*) d x cosh(2*)-sinh(2*)

A:

Q: Consider the function f(x) = 1x® %3D (a) Determine algebraically if f(x) is even or odd. (b) Based…

A: a function is even if f(x) = f(-x)  then ∫-11fxdx=2∫01fxdx

Q: +. + 1 3. Exer. 33-36: Use right-hand and left-hand derivatives to prove that f is not…

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Q: Find the first derivative of y = Arc tan √x² −1+ Arc csc x 2 O 2 O 0 2 Ox√²+1

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

Q: 1 |Leax sin(bx)] eax [a sin(bx) – b cos(bx)]+ C * Using the formula dx = ах a² + b². Sie [e-8x…

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Q: Evaluate d/dx { In√(x+1)}

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Q: S sec² (7t) tan² (7t) √1 – tan² (7t) dt

A: Given integral:- ∫sec27ttan27t1-tan27tdt

Q: Q3) Verify that the Fourier transform of the function [1–|x|, 1-|x|, |x|1 ƒ (x) = = { 1 + 0 is ƒ…

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Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: cos 2 arctan X - 1 √x+1 /x+1/

A:

Q: tan(2 – j5) j(2-j5) +7- jv2 In(-5) (320° – sin 20 + jln5)*

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Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: Linearize f(x) = 5 cos x about x = pi over 2. f(x) = -5x

A: linearization around x=a is given by :L(x)=f(a)+f'(a)(x-a)

Q: sin(2x) = - 1/2 for 0 ≤ x ≤ 2pi

A: Given query is to find the solution for the x.

Q: L {5-e²t +6t2} L {t²-3t 2e sin(3t)} MA L {t-t²-t+sin(√2t)} D

A: Laplace transformation formulas used are

Q: tan−¹(ex²) sin(√2x−1) In (x²+1) Give a definite integral that is an antiderivative of f(x) = = such…

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Q: Compute the derivative of the given function. sin ¹(³+4) O O O d dx d dx d dx [sin ¹(x³ + 4)] = [sin…

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Q: tan(2x)=1 interval [0,2pi}

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Q: 1/2 ¹/f sin¯¹ (√)—cos¯¹ (√/F) dx=? 1/4 sin ¹(√x)+cos¹ (√x)

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Q: Solve for Fourier coefficient, {6" ax 02x2n T >x 22n sin x f (x) =

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Q: Tan(3(x+iy))

A: Given below the detailed solution

Q: (1) S(1+ x² ) (2 - x) dx (2) S V? + 4 dx 3) § *³ +2x². dx x* (4) S" 5 e* + 3 sinx dx

A: Note to student : Thanks for posting your queries. But the photo contain multiple questions. As per…