Consider J x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? (A) 1/2 (B) 3/8 1/4 (D) 1

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Q: s+1) (a) L-1 4s2 +1 (b) L-1 s4 + s] (e) E{/ c{[e cos(r) dr.

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Q: How do you know that the functions sin x, ln x, and ex are not polynomials? Give reasons for your…

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

Q: 2. If f(g(x)) = sin x + 3sinx - 1, determine possible expressions for f(x) and g(x), where g(x) # x.

A: (1st method/way): Let f(x)=x²+3x-1 and g(x)=sinx Then we can find f(g(x)) as follows…

Q: Suppose f(x) =xsec²(x²). Evaluate: ] f(x)dr

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

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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 (X)> and fre)=2, f ( X) is

A: Answer and explanation is given below

Q: X Find | (х-1)(2х-1) dx

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Q: If f(x) = sin x, show that f(x + h) – f(x) = sin x cos h – 1 sin h + cos X h h

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Q: 3x2[x18 + x15 sinh(ax³)] dx

A: Given that ∫3x2x18+x15sinh(ax3)dx, 3∫3x2x15sinh(ax3)+x18dx Take u=x3→dudx=3x2,…

Q: 2-x Q.1 1 Write the function f (x) = =cosx+3x² as the sum of an even and odd functions.

A: To write the function as the sum of even and odd functions.

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: Differentiate the functions. a) f(x) = 2 – 5x + b) f(x) = e* + sinx c) f(x) =

A: Differentiate wrt x

Q: Evaluate (*(x-2) (х-1)3

A:

Q: Determine whether the function is even, odd, or neither: (a) f(x)= x* – 3x? (b) g(x) = sin(x + 1)…

A: a). Given, Now consider,

Q: Differentiate the functions. a) f(x) = 2 – 5x + b) f(x) = e* + cosx c) f(x) = d) f(x) = (5 – x²)· e*

A: Suppose f and g are differentiable function .Then note the following results : The power rule of…

Q: V3 4 dx (tan¯¹ (x)) (1 + x²)

A: ∫134tan-1x1+x2dx