Q7. Find the Laplace transform of the periodic function f(t)= sin at for 0

Q: Q3. Solve in terms of Bessel's function, the ODE: x²y" + xy' +((inx)² +) y =0 z=lnx using a Rule…

A: Here, x2y''+xy'+lnx2+14y=0,  z=lnx.

Q: Evaluate f x'V 1+4x² dx.

A: Consider the definite integral ∫01x21+4x2 dx to evaluate this, first evaluate the indefinite…

Q: 16. F(m, r) = Gm/r² at (100, 10)

A: We wil use rules related to multi variable calculus to solve this.

Q: Find the sine transform of a function of x which is equal to sin x for 0 <x<a and 0 for x2a.

A:

Q: Find the derivative dy dx dx of the function y = sec (1 + 4 + sin ¹(4 + ²)

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Q: Find F(t) such that F'(t) = sec³ (t) tan³ (t) and F (3) = 0.

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Q: Which function is obtain by shifting the graph of f(t) = sin 3t a distance of 3Tt/2 units to the…

A: Given f(t) = sin(3t)  A shift of a units to the right of t axis is given by  f(t-a)  Thus a shift of…

Q: Q2/Show that the functions is harmonic u = 2 x (1 - y)

A:

Q: If g(t)=t^2tan(t), then can the Intermediate Value Theorem be used on the interval [0, pi/4] to show…

A: If a continuous function in a domain has two domain end points and one point is above the required…

Q: Find the absolute maximum and minimum of f(t) = -2cos2t + sin4t on  the interval [0,pi/4]

A: The given function is, f(t)=-2cos2t+sin4t and the given interval is, 0,π4. Obtain the value of the…

Q: Compute the first and second derivatives of the functions: 1.) y=tan(x/3) at x = 3

A: Given; y=tan(x/3) at x=3.

Q: Let F(x) | sin (4t?) dt. Find the MacLaurin polynomial of degree 7 for F(x). 0.8 Use this polynomial…

A:

Q: V(1) (1) 20 10 + 0 -10 -2t 1 N 3 4 v(1) 5 10 7 t(s)

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Q: d Find the derivative e" + sin ax] dx e" – a cos (ax) e" + a sin (ax) e" + a cos (ax) e" + sin (ax)

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Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

A:

Q: x + 2x sin 01: Let f(x)={ . Find f'(0) if it exists. ,x= 0

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Q: Let f(x) = x°e*. Find f '(x).

A: Product rule:d(uv)dx=udvdx+vdudx

Q: 4.Find derivative y=(-2r+2)" cos(r? -1)

A: A function f(x) is said to be differentiable at x=a where a∈m, n, if: limh→0fa+h-fah A function f is…

Q: 3. Find the derivative D(x *arctan(x)) And the integral 6x dx 9+x

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Q: 5. Find the n-th derivative f(n) (x), for f(x) = e* sin(x) for all integer n.

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Q: B. Let N be the set of natural numbers, A = {1, },, 1. ..}, B = { : 1 < « < 10, where r EN}. (10)…

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Q: find the line tangent to the curve y=cos(x) at the point (π/4, 1/√2)

A: