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netineya [11]
2 years ago
6

Dy/dx y = 3root(4x+1) -2x

Mathematics
2 answers:
scoray [572]2 years ago
5 0

Answer:

Step-by-step explanation:

y = 3(4x + 1)^1/2 - 2x

dy/dx = 3*1/2(4x + 1)^-1/2 * 4  - 2

= 4 * 1.5 (4x + 1)^-1/2 - 2

= 6(4x + 1)^-1/2 - 2

= [6/√(4x + 1)] - 2

y = 3(4x + 1)^1/2 - 2x

∫3(4x + 1)^1/2 - 2x . dx

= 3 * 1/4 *  (4x + 1)^3/2 / 3/2 - x^2 + C

= 3/4 * 2/3 (4x + 1)^3/2 - x^2 + C

= 1/2((4x + 1)^3/2 - 2x^2) + C.

miss Akunina [59]2 years ago
4 0

Answer:

Step-by-step explanation:

y=3*\sqrt{4x+1} -2x\\\\y'=\dfrac{dy}{dx} =\dfrac{3}{2*\sqrt{4x+1} } -2\\\\\\\int {(3*\sqrt{4x+1} -2x}) \, dx \\\\=\dfrac{3}{4} *\int {4*(4x+1)}^{\frac{1}{2}}  \, dx      -2\int {x} \, dx \\\\=\dfrac{-3}{4}*\sqrt{(4x+1)^3} *\dfrac{2}{3}  }-x^2+C\\\\=\dfrac{\sqrt{(4x+1)^3}}{2} -x^2+C

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Using the Principle of Mathematical Induction, prove that . n ^2 − n is even for n ≥ 1​
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Base case: if <em>n</em> = 1, then

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Induction hypothesis: assume the statement is true for <em>n</em> = <em>k</em>, namely that <em>k</em> ² - <em>k</em> is even. This means that <em>k</em> ² - <em>k</em> = 2<em>m</em> for some integer <em>m</em>.

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3 years ago
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