Using mathematical induction, prove that 1²+2²+3²+ ... +n² = for all positive integers > n(n+1) (2n+1)

Q: x² tan-¹x dx

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A: whats next the pattern 6 13 24 51 142

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Q: IV. Evaluate: lim (x² + €¯²)(x-¹ csc csc z) z→0+

A: Given :limx→0+x2+e-xx-1cscx

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Q: 1. y=x² - 6x² +9x-3 2. y=2+12x-x³ 3.y=r°−2x +8r*

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A: Given problem:- the tangent plane of the surface [ x2 +y2+z2=14] at the point (1,3,2)

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Q: The function f(x, y) = x² + y² √x² + y² +1-1' (a) {(x, y) = (0,0)} (b) {(x,y) = R²2} 2 if : (x, y) =…

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Q: find the given general differential solution, using homogeneous equations with constant…

A: Given.