7. If y = y(x) is the solution of the initial-value problem_x²y + xy = 2x cos x, y(t) = 0, then_lim y(x) = (a) 0 (b) 2 (c) 3 (d) ∞ (e) None of the above.

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A:

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A:

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A:

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A: Given: f0=1, f'0=-1, g0=-1, g'0=-3 and hx=x2+fxgx. To find: h'0 Solution: Product rule of…

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A:

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A:

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A:

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Q: 1) If h(a) = a + 1, find h-(x). (A) h-(x) = 3+ (x+ 2)3 (B) h-(x) = V – I (C) h-(x) = 2a3 – 3 %3D %3D…

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Q: 3. Evaluate the derivate ax дz of the implicit equation x^sin(x) - ln(x²y) = -z²y + x

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A: Given query is to find the derivative.

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A: If  for , then to find ..

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Q: f(3) = 5, g(3) = -4, f'(3) = -2, g'(3) = 7, f'(5) = 3, g'(5) = 10 a) If h(x) = f(x)g(x), find h'(3).…

A: topic - functions and derivatives

Q: Find f"(x) if f(x) = = 25 x-4 70 (x − 4)²

A: We need to calculate f''(x) for the given function f(x). This can be evaluated as follows:

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A: We have to use properties of differentiation.

Q: a) f(x) = cos5x %3D b) g(x) = cos*5x %3D c) h(x) = cos*5x + 3x %3D

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Q: 23. If f(x)= 3x2+2x+1, find f'(2) O 6x+2 O 14+3x O 14 O 2x+1

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Q: Suppose that f and f'satisfy the following. X f(x) f'(x) Calculate 2 0 -2 4 15 -3 6 13 2 A) g' (2)…

A: (A) given g(x)=3sin(f(x))

Q: 1) If h(x) = x³ +1, find h-'(x). (A) h-'(x) = 3+ (x +2)³ (B) h-(x) = Vx – 1 (C) h-(x) = 2r³ – 3 (D)…

A: