The integral cos(x – 3) dx is transformed into , g(t)dt by applying an appropriate change of variable, then g(t) is: g(1) = {cos () g(t) = } sin () t-3) COS 2 2 O This option O This option g(t) = - sin ( g(t) = ; cos () t-5 %3D COS 2 2 O This option O hs opticn

Q: Part A (i) Let f(x) = ln(3ª + 8"). Find f'(x). %3D (ii) Find 2" cos(r)` cos(2") d da

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Q: Find f(x).

A: Given,

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Q: What is the rule of a function of the form f (a) = a sin(br +c) +d or f (x) = a cos(br + c) +d whose…

A: We are asked to find the equation of the graph.

Q: If 7'(t) = (cos t, e2t, 3t²) and r(0) = (3, 1, –2), find the function 7 (t).

A: Given. f'(t) = (cos t , e2t , 3t² ) To calculate the vector function are we need to integrate the…

Q: Let f(x) = cos(x2). Then f(20)(0) = %3D

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Q: f(x) = 3x cos ƒ'(x). -1 (2x + 4) − √√/19 − 3x², find

A: Given: fx=3xcos-12x+4-19-3x2. To Find: f'x.

Q: What is the line that corresponds to the phase shift of the function f(x)=tan (π/2 x−3π/2) +4?

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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 L {f(t)} if f(t) = cos 5t + sin 2t

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Q: The phase shift of the graph of f(t) = sin (4t - TT) is? %3D

A: We have to find phase shift of the graph of function: ft=sin 4t-π Drawing the graph of given…

Q: S(6Vx + 3 cos x - 8)dx

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Q: Let Find f(x) = y = f(x) = 5x + 18 cos x. d f(x) =

A: Given query is to find the derivative at indicated point.

Q: If f(x) = 2x cos ¹(x + 1) - √12-3x², find f'(x).

A: Introduction: Here use the derivative rules to solve the question.(1) Chain rule: (2) Power rule:

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: Find F(s). F(s) = L(1 et + 3e-4t) cos(2t)} -

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Q: J₁ exact value J Trapezoidal Rule Simpson's Rule 1 XX

A: Trapezoidal RuleSimpson's RuleWe have Hence required interval is

Q: F(s) = Le 4t cos(5t)}

A: We have to find  ℒe-4tcos5t Remember : ℒeatf(t)=Fs-a where  ℒf(t)=Fs

Q: If f(x)= cos(4x) Plot the function from (x=0) to (x=180)

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Q: fxcos (x)dx COS

A: Assume u=x^2Find du

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

A:

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

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Q: f(z) = cos(4r +5) %3D

A: we have to derivative  we know that  d(cos (ax+b) ) = -sin (ax+b) a                        = - a sin…

Q: If f(z)-6 tan , then find the value of f'(1) is 12 6 1 V2

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Q: Determine f,(x); f(x) = cos(2x³ +n²)

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