If R(x) = e*V(x) then particular solution is (a) e* T0-1) V(x) S(D-1) e V(x) S(D-1) (c) e*. 1 V(x) S(D+1) (d) e*. S(D) (b)

Q: 10. If f(x)dx = 5 and g(x)dx =-1. then (a) f(x) 2 g(x) (b) + g(x) dx = 2 (e) f(x). g(x)dx = -5 (d)…

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Q: If f"(x) = t"(x) for 0 < x < 1, then f(x) − t(x) for 0 < x < 1.

A: It is given that f''(t)=t''(x) for 0<x<1. It is known that derivative and integration are…

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Q: 57. If f(x) = (A) (0,00) fen²x + (n (ex) (n² (ex) dx; f(1) = 0 and g(x) = 1 -f(x). Then the domain…

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Q: Let f(x) I+5 f(x)

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Q: 1 •[₁ F(X) -1 Given f(x) dx = 0 and (a) [f f(x) and [₁ f(x) dx. 1 (c) [₁² (d) (b) • [² f(x) dx - [°…

A: (a)

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)?

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Q: 1. f (x² + 1)(x² + 3x) dx

A: To evaluate the given integral.∫x2+1x3+3x4dx

Q: If ƒ(x) then f"(x) = · = 0 X (t³ + 5t² + 1) dt -

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Q: (A) W f(2)-f(1) (2)-(1) QIn parts (A)-(C), find the indicated quantity for y=f(x) = 9-x².

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Q: 29. If f(x) = Eo(k + 1)¿x* for x E (–1,1) then f"(0) = 12.

A: Here, we differentiate the given function and check whether it is true or false.

Q: b) y =1+ f(z)=2x-2 O 1ks f-(z)=-1 O 2 34s (2)=2x-1

A: Step 1 Replace y with x and x with y  Step 2 Then solve for y in this equation  Step 3 Replace y…

Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

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Q: Find the approximate integral of the following function using Simpson's 3/8 rule and determine the…

A: Given: fx=ex2, x=0, 4, E=0.0002 To find: n To find: Approximate integral.

Q: What is the domian of f'(x)?

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Q: e8(x) and g(x) 43. Find f'(2) if f(x)

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Q: 6. Let f(x) = -5x¹ and g(x) = 2x + x. If h is the function defined by h(x) = f(g(x)), which of the…

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Q: (2 11) dx (x+2)* (x-1) *

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Q: 8. Find f'(x) for (a) f(x)=(x² +3x+1)(2x+3) 2x-3x+1 (b) ƒ(x)= %3D

A: We need to find the derivative of the given functions. For (a),

Q: 1. y = 4* y = 1. • 3* %3D 3. f(x) = 3*+ 1

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Q: Let f(x) = 4x - 2 and g(x) = x2 Then (f o g)(x) 3x + 4. (go f)(x)

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Q: 4+ (-1.9, 2.8) f(x) = x - 3x - x 5 -4 -3-2 -1 1 2 3 4 -3- -4 (a) (b) gure 3.21 (a) One section of…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

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

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Q: Find the Maclaurin's polynomial of degree 3 for ( a) f(x)=(1+x)e²*

A: Maclaurin Series of f(x) of Degree 3 is : f(x)=f(0)+f'(0)1!x+f''(0)2!x2+f'''(0)3!x3+...

Q: 9. [f(x)dx -1

A: Find the integral from the given graph

Q: 3 +5 - dx =

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Q: Find f'(1)when f(x) = ln(e*x").

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Q: 7. If y = e*², then d²y dx2 boins9 (A) (2x)(x² – 1)e*²-2 stod beniu (B) ex2 (C) 2xe*2 (D) (2 +…

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Q: Solve s(4- dx 3x2

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Q: r³ (x + 2) 6. Find f'(6) for f(x) = V (x + 3) Væ2 – 27 11 (a) 18 11 (b) 216 11

A: Some common derivative rules are, Also,

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: 1 Suppose f(x) = v2x + 4 and g(x) %3D 2x + 5' (f o g)(x) (go f)(x)

A: We have to find function

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.