Math Experts

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Let f and g be continuous functions of a real variable such that
g(x)= ∫_0^x f(y)(y-x)dy
for all x. If g is three times continuously differentiable, what is the greatest integer n for which f must be n times continuously differentiable?

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Which of the following is an orthonormal basis for the column space of the real matrix [(1 -1 2 -3 -1 1 -3 2 2 -2 5 -5)]

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If y is a real-valued function defined on the real line and satisfying the initial value problem above,
y^'+xy=x,y(0)=-1
(lim)┬(x→-∞)⁡y(x)=??

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Calculus playlist
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A curve in the xy-plane is given parametrically by x = t^2 + 2t y = 3t^4 + 4t^3 for all t. find d^2y/dx^2

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In xyz-space, what are the coordinates of the point on the plane 2x + y + 3z = 3 that is closest to the origin?

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https://www.youtube.com/watch?v=alebUZ8NfGE&list=PLoozEHORT1JRX5IBnT7e8otjPa_qRqhCw

Which of the following statements about the real matrix shown above is FALSE?

Which of the following statements about the real matrix shown above is FALSE?
A is invertible
det(A) = 120
If x ∈R^5 and Ax = x, then x = 0.
The last row of A2 is (0 0 0 0 25).
The matrix into the 5 x 5 identity matrix by a sequence of elementary row operations.

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Differential Equation playlist
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Laplace transform playlist
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Calculus playlist
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https://www.youtube.com/watch?v=alebUZ8NfGE&list=PLoozEHORT1JRX5IBnT7e8otjPa_qRqhCw

What is the 19th derivative of f(x)=(x-1)/e^x

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Differential Equation playlist
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Laplace transform playlist
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Calculus playlist
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Lecturer math /FPSC/AJK PSC/GRE Math / G*t subject
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For what positive value of c does the equation log x = cx^4 have exactly one real solution for x ?

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Differential Equation playlist
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Laplace transform playlist
https://www.youtube.com/watch?v=lS_5CWYfsT0&list=PLoozEHORT1JReL3O-M8jI_gjOfkSn8vZG

Calculus playlist
https://www.youtube.com/watch?v=LhjVAAkC2Ic&list=PLoozEHORT1JSo6YVPsieadnSNLRAtThvq

Lecturer math /FPSC/AJK PSC/GRE Math / G*t subject
https://www.youtube.com/watch?v=alebUZ8NfGE&list=PLoozEHORT1JRX5IBnT7e8otjPa_qRqhCw