Which 3 are functions? Why the other 2 NOT?

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2 ways: trig integral ∫sin(√x) dx

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2 ways: trig integral ∫sin(√x) dx

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2nd way: integral ∫ log √x(x^n) dx

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2nd way: integral ∫ log √x(x^n) dx

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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trig integral ∫sin(2x) cos(2x) / (9-cos^4(2x)) dx

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trig integral ∫sin(2x) cos(2x) / (9-cos^4(2x)) dx

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trig derivative differentiate x^sin(x) + (sin(x))^cos(x)

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trig derivative differentiate x^sin(x) + (sin(x))^cos(x)

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inverse trig integral ∫x^2 arc tan(x^3)/(1+x^6) dx

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inverse trig integral ∫x^2 arc tan(x^3)/(1+x^6) dx

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exp integral ∫(e^x +1)^3 dx

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exp integral ∫(e^x +1)^3 dx

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derivative differentiate x^x - 2^sin(x)

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derivative differentiate x^x - 2^sin(x)

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

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count: How many subsets does {23,24,25,...,118} have?

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count: How many subsets does {23,24,25,...,118} have?

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2nd way: trig differentiate (log(x))^cos(x)

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2nd way: trig differentiate (log(x))^cos(x)

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Difference of 2 nonconsecutive triangular numbers

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Difference of 2 nonconsecutive triangular numbers

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2nd way: derivative x^(-1/x)

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2nd way: derivative x^(-1/x)

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Properties of Determinants [examples with 2x2 matrix]

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Properties of Determinants [examples with 2x2 matrix]

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logic: Show p→q ≡¬ p∨q

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logic: Show p→q ≡¬ p∨q

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exp integral e^x (f(x) + f'(x)) dx

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exp integral e^x (f(x) + f'(x)) dx

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UC Davis #9: trig integral ∫cos^2(x)/(1+sin(x)) dx

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UC Davis #9: trig integral ∫cos^2(x)/(1+sin(x)) dx

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2nd way: derivative (x^x)^x

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2nd way: derivative (x^x)^x

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