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Q: y′=−2ex −2x2 +3x+6 y(0)=5 Solve the initial value problem above. Do not include "y=" in your answer.

A: Given that y′ = -2ex -2x2 +3x +6; y(0) = 5.That is dy/dx = -2ex -2x2 +3x +6.dy =( -2ex -2x2 +3x +6...

Q: calculate the integral of: e(x^2/2)

A: We'll use the Maclaurin series expansion for e^(x^2/2).

Q: find the derivative of f(x)= 2x^3 + 4e^3

A: Given information:The given function is

Q: What's the domain of x-1 / (1 - e^(x - 3))

A: Since this function is a rational function, the denominator can't be equal to 0.

Q: if logx y = z, which variable(s) must always be positive

A: logxy = zWith respect to logarithm:The base of a logarithm should always be positive and not equal t...

Q: The equation of the line tangnet to the graph of 24e^x at x=2?

A: Find the derivative of the given function.

Q: Determine the sum of the following series. (분) T1-1

A: we have to find sum of series .Series is given as:

Q: Evaluate the integral in cylindrical coordinates. Please see attached image.

A: To calculate the value of the integral in cylindrical coordinates which is shown below,

Q: One of parts (a) and (b) can be integrated with the Power Rule and the other cannot. Integrate with ...

A: (a) can be integrated using power rule. (b) can not be integrated using power rule because (b) has t...