ди 18. dx2 + xe-3t *, 0 < x< n, t>0 %D ди du = 0, d = 0, t> 0 dx lx=0 ди u(x, 0) = 0, 0 < x< n.

Q: 3 Evaluate 7x? dx 1 7 (Hint: f(x) = 72? and F(x) = a*) 3

A: The given integral is: ∫137x2dx Since, 7 is a constant, so take it out side. ∫137x2dx=7∫13x2dx The…

Q: Write the ratio as a ratio of whole numbers using fractional notation 12 to 1

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Q: AB1: Find g(2), g'(2), and g"(2).

A: Given that gx=∫-2x2ftdt Now we have to find g2, g'2 and g''2 In the interval -2,2, fx=4-x2In the…

Q: X x + 2 A1. The functions f and g are defined by f(x) (a) Calculate f'(x) and g'(x). d (b) Calculate…

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Q: 2) Differentiate and simplify: f(t) = 2et e2t+ 1

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Q: Exercise #3: Which of the following is a point where; (1) (0,7) (2) (-1,-1) (3) (-2,4) (4) (2,10) 7…

A: Please see the below picture for detailed solution.

Q: 8. For f(x, y) == xex²y Find fx (1, 2) {needs product rule}

A: Explanation and some important formulas:

Q: Let f(x, y) = √150 - 4x² - 2y² Evaluate f(4,0)

A: GivenA function  defined as followsAimTo evaluate the function at For a given function , the value…

Q: Suppose that the functions q and r are defined as follows. q (x) = -2x+2 r(x)=x² Find the following.…

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Q: 2) f(x) =15 - 8x A) s'(s) = B) s"(x) = x 2 C) 3x- 15 s"(x) = 8. D) s (x) = x - 5 3.

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Q: Find f. f "(x) = 1//1- x?, () - = 2 f(x) =

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Q: Consider the functions f (x) = Vx – 4 and g(x) = Vx – 4, are their domains the same or different?…

A: Find the domains of the given function

Q: Perform the indicated operation. (303-j19) (j2-1)

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Q: Let f (x) = x - 1 and g (x) = x² (x + 1). Evaluate Se 3 + dx f(x) g(x) You must show all steps.

A: Integration of e-3x+f(x)/g(x)Where f(x)=x-1,  g(x)=x2(x+1)

Q: If V=R\power{3}, and W\index{1} is the xy plane and  let W\index{2} is yz-plane:…

A: Let (a,b,c) be any element of R3, then (a,b,c)=(x,y,0)+(0,y,z)=(x,2y,z) ⇒a=x, b=2y, c=z ⇒a,b,c∈R ⇒…

Q: 7. Given f(x) = ax² + bx + c, determine the values of a, b, and c if: f'(x) = 6x + 3 and ƒ(2) = −1.

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Q: Let f(x) = g(x) = + 4, find: - X-4 a) (fog)(x) b) (gof)(x))

A: