1. Let r(t) = (t – 2, t? + 1), t = 1 %3D (b) Find T(t). (a) Find r'(t).

Q: Restrict the domain of f(z) such that it is one-to-one (if it wasn't already), and then sketch the…

A: Horizontal line test: If the horizontal line intersects the graph of a function in all places at…

Q: Please draw and make a short explanation about of this pmf : p(y) = 1/(y+1) for y = 0, 1, ..., 6.

A: Given : Equation : p(y) = 1/(y+1) defined for y = 0,1,2,3,4,5,6 The following graph is obtained

Q: DEFINITION 10.1.1 Let f be a function defined on an interval [0, o0). The Laplace transform of f is…

A: Lapalce transfermation.

Q: Q3) for f(v) = sec2(3v – 1) and g(v) = tan?(3v – 1) show that %3D %3! f'(v) = g'(v).

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Q: Find y as a function of tif y(0) = 2, y'(0) = 3. y(t) = 0 16y" + 104y' + 169y = 0,

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Q: dx If |h(0) de, then h(e) d0 : (4+x²)³

A: Given, ∫dx4+x23=∫hθ dθ

Q: Given f, S(2)dx = 4, find f,(35(2)+2) dx. S,(35(x)+2)dx.

A:

Q: d²y y = f(x) and x = e', prove that = xf'(x) +x²f"(x). %3D %3D dx2

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Q: (3) Let X = n(µ,4) and Var(2x) = E(4-7x) find u.

A: Given,X~n(μ , 4)

Q: dy / dx i

A:

Q: Find R(t) if R′(t)=⟨sint3,cost2⟩ and R(π)=⟨12,12⟩.

A: According to the given information it is required to find R(t).

Q: Find y as a function of t if 16y" + 16y + 4y = 0, and y(1) = 2, y'(1) = 3. y =

A: The given differential equation  and the initial conditions .The objective is to find the solution…

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(6) = 15, f(15) = 2, f'(15) = 7, f'(6) =…

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Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: (x+ 1) dx using the substitution of u =x +3. Vx + 3 (c) Evaluate

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Q: Find y as a function of t if y (0) = 7, y'(0) = 3. y(t) = 25y" +50y + 106y = 0,

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Q: Find y as a function of tif y(t) T y" + 16y + 80y = 0, y(0) = 5, y'(0) = 2.

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Q: Find y as a function of a if 2'y" + 6zy/ - 36y = 0, %3D y(1) = 1, y(1) = 5. %3D y =

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Q: (7x² +7x) dx

A: The objective is to evaluate the integration

Q: dy (x³ + 1)(x² – 2x-1+ 1) of y = dx x² + 3

A: y=(x3+1)(x2-2x-1+1)x2+3

Q: f(x) dx = 18 and f(x) dx = 3.7, find f(r) dr.

A: using property of definite integration

Q: dx Find F(x) = S 1-2x+ 2x2

A: Here we solve the integration problem.

Q: (f) ef +1 ex dx

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Q: Sove for dy 4 X3 hy= e*csch (2-y?)

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Q: 3 dx%3D 2 (x-1)(x+2) Select one: a. In(5/2) b. -9/20 c. In(8/5) d. -33/20 e. In(2/3) 3.

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Q: Find y as a function of t if y(0) = 8, y'(0) = 4. y(t) = 6y" + 33y = 0,

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Q: dx xy dy x² + y² Ans. y² = 2x²ln (

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Q: dy = 4x -3 and y(4) = 0. dx Find the function y(x) satisfying

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Q: b) Evaluate f v1 – x² dx.

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Q: d (coth x)= dx

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Q: | (e-x + vx)dx 1. 2. x²)dx

A:

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.