Evaluate the integral. x/2 [3 cos ti-2 sin 5t j+ sin² 5t k] dt 0

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A: The Solution is given below:

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A: NOTE: Refresh your page if you can't see any equations. . the given equation of the line is

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A: To express the limit limn→∞ ∑i=1n i4n5, as a definite integral.

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A: Given query is to find indicated derivative.

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Q: 11. fx² cos(x³) dx

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Q: The equation of the ellipse that has a center at (6, 1), a focus at (10, 1), and a vertex at (1, 1),…

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Q: (x²–2x+11)dx (x²+3x-4)

A: The given integral is: I=∫x2-2x+11x2+3x-4dx   Use the common integral. ∫1ax+bdx=1alnax+b+C

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A: Given: y=5x4-5x2+64 Formulas: ddxxn=nxn-1ddxconstant=0ddxfgx=ddgxfgx·ddxgx→chain rule

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Q: If a cup of coffee has temperature 92°C in a room where the ambient air temperature is 23°C, then,…

A: This question can be solved using the concept of average value of a function in a given interval.

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A: Given query is to simplify the expression.

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A: Here we have to apply cosine law.

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Q: Given y = √x. Find dx dt 11 dx - dt when y = 3 and (Simplify your answer.) dy dt 1.95.

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A: Let's convert given rectangular point to polar coordinates.

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A: The given function is  f(x)=2x-3,x=2  and  ∆x=2

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Q: 2 2 Suppose f(x) dx = 7 and f g(x) dx = -5. -1 -1 2 Evaluate S (-2 f (x) - 3 g(x)) dx. -1 Remember…

A: given  ∫-12f(x)dx=7 ∫-12g(x)dx=-5∫-12(-2f(x)-3g(x))dx=-2∫-12f(x)dx-3∫-12g(x)dx

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A: Given f( t ) = F'( t ) F( t ) = t3 + 6t a = 2  &  b = 6

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A: Using chain rule of differentiation

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Q: if f (X) is a Linear function € (-5)--3, and ECD) = -4 Find an equation for E(X)=

A: Given data÷ Function fx is linear function. f-5=-3 and f1=-4

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Q: 19) tan [Arcsin ()] 2

A: Solution ⇒     tan⁡(arcsin⁡(32))  =?    First, we will solve  arcsin⁡(32)    We know…

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A: Given query is to find the slope of the line and it's meaning.

Q: Find f such that f'(x)=x²-6 and f(0) = 8.

A: The given data is: f'x=x2-6 and f0=8 To find the value of fx.

Q: The marginal profit in dollars on Brie cheese sold at a cheese store is given by P'(x)= x (50x² +…

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