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

A: Derivative of function

Q: s sin(3x) + cos(5x) – sin sin)ax |dx

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Q: If f(x) = cos(2x) then find II f (t|4)

A: Given query is to find the Indicated derivative.

Q: Sketch the following (without using calculator) and find their domains and ranges. (1) y = cotx (2)…

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Q: g(x) = cos(x + T) + 2 %3D

A: The given expression is gx=cosx+π+2.

Q: Y₁' = 3Y₁ + 1/₂ ل3 Y/₂ = 2y + 2y₂

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Q: 9. Please help!!   Choose the point or points that are inflection points.

A: The inflection point is a point where the concavity of the function changes. That is, if x = a is…

Q: cos 2x dx (b) 4 cos t dt 0 2

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

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: Suppose S (x) =sin(3x – 2). Evaluate: /f(x) dr A - 3cos(3x – 2) + C (A) (B ® --cos(3r – 2) + C ©…

A: Given, f(x) = sin3x-2To evaluate:∫f(x) dx This can be done as follows:

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: (4) Evaluate cos (2x) -dx. (x² + 1)² 8.

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

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

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

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Q: If f(x) = cos(2x), then f"|

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

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Q: f(x) = 5 sin²(x) Hint: Use sin2(x) = -(1 – cos(2x))| %3D %3D n = 1 8.

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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 y = 2 sin ( 3x+ n) –1 , The range is : (- 3,1) O (-1,3) O (-2,2) O (-3,3) O

A: the given function is  y = 2 sin3x+π-1

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

A: Solution of given question is followed by:

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

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

Q: Find f if f" (x) = 2 + cos(x), f(0) = -8, f(T/2) = 8. *(x) :

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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: 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: If f(x)-logCos4x + sinx.Then find 9 (x) JP at x= sec 2c dx 6.

A: Given function is: f(x)=logsec2x|cos4x|+|sinx| To find the value of 9df(x)dx at x=-π6

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…