Solve the following initial boundary value problem au ou 0 ), (0,1)=u(z,1) = 0, (>0, u(x.0) = f(x), (x,0) = 0, 0

Q: 2) f(x) = xx| - T <x<T Ans. Odd

A: the given function is  f(x)=xx

Q: 7. f(x)= // at x = [0, 1]

A: Given: fx=1ex3 ,x=[0, 1] To find: n when error E=0.0002. To find: Approximate integral by using…

Q: 3. Vectors u and V are as shown, forming an angle of 30°. Describe the vector u x. = 5 units, and v…

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Q: A shopper buys cat food in bags of 3 lbs. Her cat eats 3434 lb each week. How many weeks does one…

A: Given that A shopper buys cat food in bags of 3 lbs. Her cat eats 3/4 lb each week

Q: Find the value of the derivative at each relative extremum shown in Figure 4.3

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Q: 5. Since /1+ f'(x)² > 1 for any function f, we have length of graph of y = f (x) over [1,4] = 1+…

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Q: (*+ (H)')" 0.8 f(x, y) = %3D af 1.6x(x^2+(y/9)^2Y^-0.2 af 1.6/9y(x^2+(y/9)^2)^-0.2 ду

A: Using partial derivative rules

Q: Problem 4: Perform a first derivative test on the function f(x) = 2x + 6x a) Locate the critical…

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Q: A function h(x) = = Compute h'(3) if x-2 f(x) f'(3) = 2 and f(3) = 1. is defined in terms of…

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Q: (2, 1) Graph of f The derivative of a function fis defined by f'(x) =/1-2 in (2-), -5≤x≤2 where the…

A: Since you posted multiple question, we will solve first question for you. Kindly repost other…

Q: 7. If g(4) = 3k +7, g(9) = 7, g' is continuous and %3D J g'(x)dx = 2k? + 13, find the value of k.

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Q: of n if each function had to ensure that the error of the method is 0.0005 find the approximate…

A: We will use formula for trapizoidal rule and its error

Q: If f(x) = (sin(x) S 4 + t dt and g(y) = = [ f(x). f(x) dx, find g^(1). 6

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Q: 5 True or falce: F F(x) = f(g(x)) and f'(2) = -1³ 3 given that (9): 2, g'(a)=3, f'(9) = 3 こ

A: The given values are  and .We have to determine whether the statement is true or false.

Q: Given the graph of the polynomial function, determine its equation: 6- 4 2- 0 -2- -4- H 2 3 4 X

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Q: 5. A function f satisfies f'(-5) = f'(5) = 0; f'(x) > O in the interval (-5,5) ; f'(x) O in the…

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Q: if x² + y² =t -- and x* + y* = t dy prove dx 1

A: Given, if  x2+y2=t-1t and  x4+y4=t2+1t2 To prove that  dydx=1x3y

Q: 6. Find all critical numbers and use the Second Derivative Test to determine all local extrema. a)…

A: for part a see 2nd step. for part b see 3rd step.

Q: Show that so that [*_da'ƒ (a'ſõ(ª − ¶') = ™** ªqÿ(¶')ƒ(q − q'), ƒ®ğ=gof.

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Q: 7.The rate of contamination in a certain lake is C'(t)=tln(2t) hundreds gallons per month, where t…

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Q: -1, if -n <x<0 1, if 0sxSa h) f(x) = { %, -1<x<0 0<x<1 -x, if %3D if

A: We find Fourier coefficients then find required Fourier series.

Q: 1(4) = , re) = -2 x + 2 2(т — 1) 3 f' (x) = 3 and f"(x) = %3D 2(x – 1)2' (x – 1)³ * Find all local…

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Q: 3. Let f(x) = ={ and x² if 0≤x≤ 1 √2x-x² if 1<x<2 A graph of y = f(x) is shown in the figure. (a)…

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Q: Draw graph of a function which satisfies the conditions below. f'(x) 0 on interval (5, 7) f'(x) = 0…

A: As informations are given only in domain 0 to infinity so let's draw the graph form given datas…

Q: 1. Find derivative, critical numbers and the absolute maximum and absolute minimum values of f(z) =…

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Q: - Find f' where f is defined on [0, 1] as indicated: (a) f(x) = , VP + dt %3D 1 (b) f(x) = c cos dt…

A: Solution by using fundamental theorem of Calculus

Q: 1 2 3 f(x) 2 4. 3 4 1 g(x) 4 (2),6 h'(2) if h(x) = f(x) g(x) f(z) h'(2) if h(x) = g(x) h'(2) if h(x)…

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Q: (b) Find Rz (t) in terms of R(t),s SsS

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Q: a) Suppose that f(3) = 15, f'(3) – 5 and let H(x) = Vf(x)+ 10. Find H'(3). b) Let f(x) = cx +…

A: (a) Differentiate the function Hx with respect to x to find H'x.