Consider the following three functions: f(t) = sin((t-2)), g(t) = ㅠ sin ·(t — 4)), 31 ) = sin((t+1)). h(t) = Use congruence properties to find a positive value for t for which all three functions are simultaneously equal to 0. Explain your reasoning carefully and show all of your computations.

Q: 2. a) Find a formula for f-1 for the function y =f(x) = (x – 2)2 , x< 2 b) Evaluate the expression…

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Q: Show that J (x) = 2 sin x

A: By definition,                  . Now,  we need to prove the above statement by taking n = 1/2.

Q: for 2 sin (xy t 22) W ニ

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A: Polynomials have finite terms. And it has a highest degree.  But sinx , lnx and ex have infinite…

Q: d Find tan1 x + csc¯1 | dx

A: To find ddxtan-1x+csc-1x We know that ddxtan-1x=11+x2 ddxcsc-1x=-1xx2-1

Q: cos2x – sin2x cos2x For +C: What is F(x)? dx= 3 cosx - sinx

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Q: Evaluate S₁ 45 dx 1- cos (9x)

A: To evaluate .

Q: Evaluate § A² B³ dx where A = sin(f(x)), B = cos(g(x)), and f(x) = g(x) = 4x.

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Q: The function p(t)- 20 sin 2xt + 100 models a person's blood pressure while resting, where p(t)…

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Q: Given the functions fz) = 3* and g(x) = sin x, determine the domain of the combined function y=…

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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: Let a<b. Use an important theorem to reason that t  | y(b) − y(a) | ≤ 3000(b − a).  The function is…

A: Step:- 1 Mean value Theorem :- Let f be a continuous function on [a, b] and function is…

Q: Sketch the graph of the function f(x) = 12 x sin x on the interval [−3π, 3π]

A: we have to sketch the graph of the given function at the given interval. f(x)=12xsinx on the…

Q: Find an analystic function whose real part is e-x (x sin y-y cos y)

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Q: √√3 tan-¹x 4. (10 points) Evaluate SY 1+x2 dx (using substitution).

A: The value of the integral is 7 pi^2 / 288.

Q: (2) Let f(x) = -3 sin (r +). (c) And then determine the domain and range of f(x).

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Q: For f(x)=cosx+sinx, determine all of the values of x for which f(x)=0

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Q: Evaluate L{2t e2t sin (3t) – e3(1-1) + 3et sin (4t – 5)}

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Q: Derive the expression  F1− F2 = (F1 − Fc)exp( f φ) − 1/exp( f φ) using the equation (F1− Fc/F2− Fc)=…

A: Given that, F1− FcF2− Fc= efφ To derive F1-F2=F1 − Fcefφ-1efφ. Consider, F1− FcF2− Fc= efφ Then,…

Q: Use Cayley-Hamilton theorem to find (i) the inverse of A = (ii) A

A: This question is related to matrix, we will solve it using given information.

Q: Find all solutions Cos(x/2)-cosx = 0

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Q: Drive the following function for :(y) 3(sin(2xy))²

A: We have to find the derivative .