Let X=L'[0,1] and x=2()- Find Ilallp for P-4 and ∞

Q: Find y as a function of a if y" – 8y" + 15y/ = 8e", y(0) = 28, y(0) = 14, y"(0) = 12. y(x) =…

A: We have to find the solution of differential equation.

Q: Let f(x)=x^2−8x+5 with domain 0<x<4 Calculate (f^−1)′(−2)

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Q: Let f(x) = 6 + V4x – 5. Find f-'(x). f- (x) = for x > 6

A: Given f(x)=6+4x-5 The objective is to find f-1(x).

Q: Let f(x) = x7 Then f'(x) is 5æ5 + 3x³ – 3æ – 4. За — - - f'(3) is f' '(x) is and f''(3) is

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Q: Find the absolute maximum/minimum if any of f (x)=x' +3x² +1 on the interval [-3, 2].

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Q: Q-1Find the derivatives of the functions 1- Y+In (xy) =1 2. Inxf 9.

A: Note:- Derivative of the product of two functions is ddx fx·gx  =f'x·gx+fx·g'x   Part (1):-  Given…

Q: Find the x-coordinates of all of the points on the graph of f (x) where the derivative equals 0.…

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Q: The domain of the function f(x)= tanh(18 - ) is (289, A), Then The value of k= %3D The value of A =

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Q: Consider the interval [-2, -1].  According to the Intermediate Value Thereom, which of the following…

A: Intermediate Value Theorem:- If a function f(x) is continuous on the interval (a,b) and have value…

Q: (4³ + 6)%,' = x^(,5 + 6)5 y

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Q: lim (x' – 2x* +5)= x→-2 O a. 22 O b. -11 O C. -13 O d. -18

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Q: For the function f(x) =-X find f"(X), f"(0), f’"(1), and f"(- 1). "(X) = O I7

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Q: Example 4. Differentiate with respect to 'x': 2 - 3x + 4 - X + x + 2

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Q: find all pairs (m, n) of positive integers such that ϕ(ϕ(n^m)) = n, where ϕ(n) is Euler's totient…

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Q: Now, differentiate the function y' = 4x(1 + 2 In). y" = 4 + 8 + In + 8 In

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Q: + If x? = x-y then, y *+y

A: Given  x2=x+yx-y first we multiply each side by x-y x2x-y=x+yx-yx-y     by dividing  x-y from x - y…

Q: Assume that for a function f(x), f'(x) « O on the interval (-0, -5) and f'(x) » O on the interval…

A: From the given definition:  f ' (x) &lt; 0 when x &lt; -5 so graph must be decreasing in this…

Q: _____18) Find y' if y= 6+x √4-x²

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Q: If x' x= [(-₁)] and x(0) = [] x what is X(T)?

A: Given: x'=01-10x and x(0)=01. To find: x(π)

Q: If Ax) = 2x+ 1and g(x) = x, Find g0)) %3D

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Q: Use the graph of fand g. Let p(x) = f(x)g(x) and q(x) = -2 10 8 6 4 2 (a) Find p'(4). p'(4) = (b)…

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Q: y' = 8|x| = - 8x, x≤0 8x, x>0

A: To find y'' and graph the general shape of f(x), we first need to integrate the given expression for…

Q: Given the graph of ƒ' (x) below, where the Dom f (x) = (-∞, ∞) . Find ALL interval(s) for which f""…

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Q: Substitute the value of y' in 1 + (y)²

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Q: Let y = || = y'"' = = x + 7 X X Hint: Try to do this without using the quotient rule.

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Q: Show that the f(x)=x-(In x)^{x} =0, has at least one solution in the interval [4, 5]. O f(4)=0.31,…

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Q: Find y '  if  x  3+ y 3= 6xy

A: Given: x3+y3=6xy for finding y', we differentiate given equation with respect to x so,…