1 (1) u(x) = x + f * u(t)dt, u(x) = x+ 24 2 (2) u(x) = ² = x + √² xtu(t)dt, u(x) = x (3) u(x) = x + [xtu²(t)dt, u(x) = 2x

Q: If f(x) = f'(x) = 1 x³ 3 √t² + 1 dt then F

A: Here we will use the Leibniz theorem to  find the derivative of the given problem, so on using this…

Q: What is tl

A: Given function is: f(x) = 3 + cos (3x) We have to find the gradient of the function.

Q: f(x) = (13 + 6t² + 1) dt

A: SOLUTION-

Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

A: our objective is to find the required derivative

Q: If f(x) = 1+/x, then f'(x) = -1 A 4/xV1+/x 1 B 4V1+x 1 4/x/1+Jx 1

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Q: If f(x) x = √₁² (2²³ + Sº (t³ + 5t² + 2), dt then ƒ''(x) = =

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that Find F'(8) and G'(8). = F'(8) = G'(8) = ƒ(8)…

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Q: Find a function f(x) such that f'(x) = − 5eª + 3x and ƒ(0) : = f(x) = - 1

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(9) = 13, f(13) = 3, f'(13) = 12, f'(9)…

A: Given: Let F(x)=f(f(x)) and G(x)=(F(x))2 And f(9)=13, f(13)=3, f'(13)=12, f'(9)=10

Q: x²+2x=1 then f'(1) is Let f(x) = 2x3+1

A: we have given f(x). And we have to find f'(1)

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(4) = 11, f(11) = 3, f'(11) = 8, f'(4) =…

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Q: Find the maximum and minimum of f(x,y) = yx2 + y(y - 1)2 subject to x2 + y2 =1.

A:

Q: Find a function f(x) such that f'(x)% = - 3a? + 8 and f(0) = 1 f(z) = %3D

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Q: If f(x, y) = (5x- y²) (a) f(1,4) find the following.

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Q: 8. Find f(4) if f(0) >0 and [f(x)]² = [(f(t))² + (f'(t))²]dt + 4.

A: We do this using Lebniz rule for differentiation under integral sign. The detailed solution is…

Q: Find the centroid of the region bounded by the graphs of the functions y = 7x², y = x² + 2 The…

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Q: F(x) = f(f(x)), G(x)= (F(x))2 f(6)=11, f(11)=2, f'(11)= 14, f'(6)=14 F'(6)= ? G'(6)=?

A: given: F(x)=f(f(x),  G(x)=(F(x))2 f(6)=11,f(11)=2,f'(11)=14,f'(6)=14

Q: 15 [ = f(x) = H t²dt then

A: f(x)=∫x15t2dt

Q: Assume that  dx1/dt= x1(10-2x1-x2) dx2/dt= x2(10-x1-2x2) a) Graph the zero isoclines. b) Show…

A: Given- Assume that  dx1dt = x110 - 2x1 - x2dx2dt = x210 - x1 - 2x2 To find-  Graph the zero…

Q: If f(x) - Sto = t5 dt then f'(x) = and ƒ'(−4) =

A:

Q: Let F(x) = f(f(x)) and G(x) = (F(x))? and suppose that f(9) = 7, f(7) = 3, f'(7) = 14, f'(9) = 3…

A: topic - functions and derivatives

Q: Find f such that f'(x) = f(x)= f(16) = 21.

A: Topic:- application of integration

Q: By direct differentiation of x(t) = eAtxo + eA(t-o) Bu(o)do show that ¿(t) = Ax(t) + Bu(t), x(0) =…

A: The differentiation of a definite integral can be obtained by using the Chain Rule following…

Q: In this problem, y = c₂e + c₂ex is a two-parameter family of solutions of the second-order DE y" - y…

A: The given problem is related with differential equation. Given that y = c1ex + c2e-x is a…

Q: If f(x) = then f"(x) = = X √ ² ( 2³ + (t³ + 4t² + 5) dt 0 ←

A: Let,Using integration formula So,If  dtPut , dt = F(t)Then So,