An electrical signal is given by the function y(t) = sin(Pi*t). Determine the root mean square value of this signal between t = 0, and t = 1/2.

Q: Find the average rate of change of the function over the given interval. f(t) = 13 + cos t a. - T, 2…

A: given f(t)=13+cos(t) To find the average rate of change of f(t)

Q: Find the differential of the function. Y = e2x

A: Given function is  y= e2x

Q: Find the differential of each function. (a) y = tan(7t) dy = 3 - v2 (b) у 3 3 + v2 dy =

A: topic - differential equations

Q: Find the indicated derivative or integral a. D, (3** * ) c. D, log,, (x³ +9) –3x а. D, b. |x 2* dx…

A: We know that Dx ax = ax·ln(a) Dx af(x) = af(x)·ln(a)·f'(x)   ∫ax dx = axln(a)+C   Dx loga x =…

Q: Find the length of the curve y = In sin x from t = -2 to t = 0.

A:

Q: Find the indicated derivative: d/dt ((e^t ,e^(2t),e^(3t)) X (sin(t),cos(t),tan(t)) )

A: We have to Find the indicated derivative of ((e^t ,e^(2t),e^(3t))(sin(t),cos(t),tan(t)) )

Q: 4.62. Evaluate the derivative of the Gamma function and see dT'(x) r'(x) = dx ' (In t)e"'dt

A: To differentiate the gamma function:         Γ(x) = ∫0∞tx-1e-tdt Integral definition of gamma…

Q: Find the differential of the function. y= e^x /  1−e^x

A: We have to find

Q: 7n Find the average rate of change of f from t to 2 f(x) = cos 2 %3D

A: The average rate of change of the function is:

Q: 1. Find by implicit differentiation (a) e=/y = x – y (b) sin (x + y) = COs r + Cos y

A:

Q: The average rate of change of f(x) = sin(x) with respect to x as a changes from 0.5 to 1 is O 1 0 2…

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Q: Eliminate the parameter f) from the following X(+)= -sint yl)= cost

A:

Q: ÿ + ỷ = sec t tan t

A: This is the question of the differential equation.

Q: If the PSD of X(t) is S„(@). Find the PSD of dX(t) dt

A:

Q: Find of the following by implicit differentiation. Show solution. dx y sin x =x2 – 2y • sin x+ sin y…

A: This question is related to derivative.

Q: Find the second derivative of the function. h(t) = 10 cos t − 15 sin t

A: Given: ht=10cost-15sint for finding second derivative of given function, initially we find first…

Q: Find e dx approximately using Simpsons rule with n 10.

A:

Q: (b) by using gamma function x-1/3e-Bx dx

A: Gamma function

Q: Find the linearization of the function f(x) = sin(x) at a = π and use it to approximate the number…

A:

Q: Evaluate in terms of beta function: L (1– 1) dz dr. O-)

A: According to question given:∫01(1-1x)13dxWe have to evaluate the given integral in terms of beta…

Q: Find for the following function: dx 1- y = sin-1 2x + 3

A:

Q: nd the equation of the normal line at x = given g(0) = 2 cos 0 + sin² G

A: We have to find

Q: Given a function ƒ that is differentiable on its domain, write andexplain the relationship between…

A: The differentiable function is f on the interval I which contains a point a. The linear…

Q: The derivative dy for the function %3D (1i) y= cot リーCof V-x

A:

Q: The slope of the tangent line to the curve at (x,y) point is defined by (1+ k) e2a+e .If the curve…

A:

Q: Find the normalizing constant c so that ce-x/4 dx = 1. C =

A:

Q: Find the differential of each function. (a) y = tan(3t) dy =

A: We have given  y= tan(√3t)  We have to find the differential equation.

Q: A point is moving along the graph of a given function such that dx/dt is 6 centimeters per second.…

A: Given Take derivative with respect to t, derivative of y is dy/dt  and derivative of x is dx/dt

Q: Evaluate the function: ( e* +1 dx et

A:

Q: Find the differential of the function y = V1+ cos(0)

A: Find the differential of the function

Q: The height of an arch above the ground is given by the function y = 11 sin x for 0sxSr. What is the…

A: This question can be solved by applying the formula of average height of an arch.

Q: Differentiate the function. y (x) = esin 2x + sin(e2")

A: It is given that, yx=esin  2x+sine2xWe have to differentiate the given function.

Q: The slope of the normal line to the tangent line of 1 is f(x) = (sin x)² at a = V2 :Select one V2 .a…

A: We have to find slope of normal to the tangent line of fx=sin-1 x2 at x=12. We know the slope of…

Q: 4. Find the indicated higher-order derivative of the given functions. d'y а. у %3D 8е* + sin x; dx7…

A:

Q: Find the general antiderivative of the given function. sin( x/7π)   and  sec2(5x) + sec2 (x/3)

A: GIVEN DATA : Function sinx7π and sec25x+sec2x3        TO FIND : Anti derivative of the function…

Q: Find the average rate of change (AROC) of the following functions over the interval [60 ≤x≤180] y =…

A: using , average rate of change…

Q: Sin (7€) + Cos (SE) 5지

A:

Q: The height of an arch above theground is given by the function y = 10 sin x, for 0 ≤x ≤∏.What is the…

A: The height of an arch above the ground is given by the function y = 10 sin x, for 0 ≤x ≤∏.What is…

Q: Find the derivative of the function. - c() (수 1 - e9x 1 + e9x y = cos y' = 18e9z sin + e&= )…

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Q: Integrate the function. dx Jzx (1+x) A sin-1 +C tan-1 C In |x|•C D tan-1 .C

A:

Q: 10. Let y = In(x' + sin 3x). Find dy/dx.

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Q: The function f(z) = e-y sin x is harmonic function

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Q: 2. Find the first and second derivatives of the following functions a) y = 6) y = e", c) y = In (sin…

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Q: Consider the implicit function. ev = sin (2x) dy in terms of x. dx Determine the formula for dy dx

A:

Q: Find for the following function: dx 1- y = sin-1 V2x + 3

A: See the attachment

Q: Vye-y² dy

A:

Q: Find the differential of each function. (a) y = tan 3t dy =

A:

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. Round…

A: cos32° It can be written as, cos32°=cos30°+2° Now, fx=cosx, x=30° & ∆x=2°=2π180 radians Now…

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. Round…

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.