Solve the initial value problem y' = 5y + 3xy6 with y(0) = 1. y(x)=1/√√f(x) with f(x) =

Q: 12. Consider the equation x = ( 1 ) x x' -5 -3 Express the general solution in terms of real valued…

A: The given system of differential equation is:x'=1-51-3 x

Q: Let h(x) = f(x)g(æ). If f(x) -3x? – 4x + 2 and g(x) = -x² + 3x +2, what is h' (-1)? Do not include…

A: Given, h(x) = f(x)g(x) f(x) = -3x2 - 4x +2 g(x) = -x2 +3x +2  We have to find h'(-1)

Q: f(x) = x²e²

A:

Q: 15. With f(x) = 3x +1 and h(r) = 2x – 4, find (f oh)(5) - %3D

A: we know that  (fog)(x) = f (g(x))

Q: Find the GS for x³y"" + 6x²y" + 4xy' — 4y = 1 − x − 2x² -

A: Solution:-

Q: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

A:

Q: If h(x)=√ 7 + 6f(x), where f(1)= 7 and f (1)= 2, find h(1). h'(1) = x

A: Given function Where

Q: y-y1=m(x-x1) y-(-1)=4/5(x-(-1)) y+1 = 4/5x + 4/5 y=

A: The given equation is y+1 = 4/5x+4/5      y = 4/5x+4/5-1         = 4/5x-1/5

Q: If R'(x)=250-18x and R(0)=0, find R(x)

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Q: 1 f(x) = 1– 3x

A:

Q: Suppose f(-10) = -9 and f'(-10) = 8. Find the following. d (10x² + x − 9) ƒ(x) at x = − 10 is dx d…

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Q: Find F'(x). 1. F(x) = √x+² (4t + 1)dt 2. F(x) = f*t³dt SOLUTION IN HANDWRITTEN

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Q: (c) J2 +∞ dx 2 x ln² r

A:

Q: If f(x) = =√(t³3 + 3t² + 6) dt then f"(x) =

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Q: 1. Find the function f(x) if f'(x) = 3x² – 2.x +5 and f(0) = 5 %3D

A: Given, f'x=3x2-2x+5f0=5 To find, The function f(x).

Q: Given f(x)=-25sin (Sx) and f₁0) = -5 and f(0) = 4 Find F(1) 2

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Q: 2x-3 3x (x-3)2 find the x-value(s) where k'(x) is (are) undefined. If k' (x) : for all x in the…

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Q: '5 '5 '5 If f(x) dx = 33 and g(x) dx = 14, find [2f(x) + 3g(x)] dx. %3D

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Q: If fx)=5x-1, g(x)=1/x, and h(x)=g(fx)), then what is h'(0)?

A: Given that h(x)=g(f(x)) Using chain rule we get: h'(x)=g'(f(x))f'(x) We plug x=0 So,…

Q: Find h'(x) given h(x) = 6x√√x. 3 O ○ 6x² 09√x 6x7 6+x7² None of these

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Q: 3-5x 11. Find f'(x), if (i) f (x) = (x² – 1)(x5 + 2)+/3, and (ii) f (x) (x3+2)1/3*

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Q: Find f'(x). f(x) = (x² + 1) * f"(x) = %3D

A: Find f''(x)

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,

Q: h(x) = px³ + 4px + 1, where p and q are constants. Given that h(-1)=-41 and h'(-1)=67, find the…

A: h( x ) = px3 + 4px + qxh( -1 ) = -41 h'( -1 ) = 67

Q: If f(x) = 5x4 – 2x3 –x² + 3x – 1, then | f'(0) = d2 ;f(0) = dx f"'(x)= d4 ¡f(x)= dx

A: