What substitution should be used to solve the integral O sinu=3x/2 O sec u =2x/3 O sec u =3x/2 O tan u =2x/3 x² dx 4-9x²

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A: 1.the formula of derivative of two function is fg'=fg'+gf'

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A: Solution is here

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A: SOLUTION-

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Q: In evaluating x=3.98. dx x²-9 is same as evaluating lim (In(f(x))). Determine the value of f(x) if…

A: First we evaluate f(x) using substitution

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Q: Find the absolute extrema of f on the given interval. (find the absolute maximum value and absolute…

A: We know that, Suppose that x=c is a critical point of fx then, If f 'x<0 to the left of x=c and f…

Q: Consider the function f(x) exact values. f'(x) = f''(x) = f'''(x) = = Compute each of the following.…

A: Topic:- derivatives

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Q: 11.J sin 3 x sin 6 xdx 3

A: To evaluate the given integral.∫sin 3x sin 6x dx

Q: Question 19 Given f(x,y) = ex cos y, Evaluate fx(0,2) A) e² B 0 (C) -sin 2 D) cos 2

A: Topic = Derivative

Q: 1. Evaluate the given integral Q. Q - L. f.²² (y - 2x^²) dz dx dy Your answer

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

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Q: y = ln √4x² (Hint: Apply first a property of LOG.)

A: Let's find first derivative.

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Q: 14, which 12 54 32 9 27 of the following rule defines y as a function of X 13 18 101 69 350

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A: Here we need to find out the domain of the given function.

Q: 2 Find all local extreme values of f(x) = -2.3 + 11x² 56x + 30. 3 The FIRST local extreme value,…

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Q: 6. f In² x dx

A: Topic = Integration

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A: Please follow the next step.

Q: 1. J x + 2)* dx A. (x + 2)6 + C О А о B о B. 6(x + 2)6 + C (x+2)6 6 + C

A: As per guidelines we can answer only one question at a time, so the first question can be solved as…

Q: 18) lim xcos X

A: limx→∞xcos1x

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Q: Question 2 Iff and g are continuous on [a,b], then t True B) False in √ [f(x)g(x)]dx = {√°f(x)dx)(√°…

A: Given that f and g are continuous function on [a,b].

Q: Suppose that fn ⇒ f on R and that each fn is a bounded function. Prove that f is bounded.

A: Solution

Q: 1. √2x+1 -15 2. So √x+1dx -0.5 3. 5x(1-2 4. fx√x-3 5. fx √x+1

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Q: Find the absolute extrema of f on the given interval. (find the absolute maximum value and absolute…

A: Given, x2+ 4x+2, [-3,0]

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A: Solution

Q: (b) In +8 x² 2 - 36

A: We have doing solution useing logarithm laws

Q: Using Fundamental Theorem of Calculus (FTC). Compute the following

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Q: tan² y = x (By implicit differentiation)

A: The given equation is tan2y=x.