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Q: A theorem states that one local extremum implies an absolute extremum. Verify that the following fu...

A: The given function is,

Q: Use spherical coordinates to find the volume of the region outside the cone phi= pi/4 and outside th...

A: To calculate the volume by using the spherical coordinates of the region outside the cone φ=π/4 and ...

Q: Help please.

A: The given function is (tan-1x)2.

Q: for the function f, given below, find the antiderivative F that satisfies F(1) = 1 The antiderivativ...

A: First, we find the general solution using integration.

Q: How to convert percentage to ratio?

A: In this question we have to explain how to convert the percentage in fraction form.

Q: y = t(lnt)2 Find the derivative

A: According to the chain rule of derivative,Using the above rule, where u = t and v = ln t

Q: During the first four months of employment, the monthly sales S (in thousands of dollars) for a new ...

A: Part (a)S= S(x)= 9 / x + 10 + x / 4, x ≥ 4The given function is defined only for x ≥ 4. We don't hav...

Q: 1) The substitution u = tanx gives∫(sec2x.tanx)dx = ∫(x)du = 1/2.u2 + C = 1/2.tan2x + CThe substitut...

A: Yes, both integrations are correct by their respective substitutions.Reason:An integral of a functio...

Q: If p 8m2-9m + 3, then the rate of change of p with respect to m when m 1 is 16. 1 -9, 7. 2.

A: Approach:A clear relationship between "p" and "m" is given"p" is dependent variable while "m" is the...