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SUBHASH PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -FIVE MARKS QUESTIONS WITH ANSWERS
- If y = A sin x + B cos x, the prove that (d^2 y)/(dx^2) + y = 0
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- If y = 3e^(2x) + 2e^(3x), prove that (d^2y)/(dx^2) - 5(dy)/(dx) + 6y =...
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- If y=(sin^(-1)x). Show that (1-x^(2)) (d^(2)y)/(dx^(2))-x((dy)/(dx))=0
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- If y=3 cos(log x)+4 sin(log x), show that x^(2)y(2)+xy(1)+y=0
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- If y=5 cos x-3 sin x, Prove that (d^2y)/(dx^2)+y=0.
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- If y=Ae^(mx)+Be^(nx), prove that (d^(2)y)/(dx^(2)) -(m+n) (dy)/(dx) + ...
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- If y = (tan^(-1)x)^(2) then show that (x^(2) + 1)^(2) (d^2 y)/(dx^2) +...
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- If e^(y)(x + 1) = 1 show that (d^2 y)/(dx^2) = ((dy)/(dx))^(2).
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- y = 500 e^(7x) + 600 e^(-7x) prove that (d^2 y)/(dx^2) = 49y.
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- If y = e^(a cos^(-1)x), -1 le x le 1 show that (1 - x)^(2) (d^2 y)/(dx...
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- If sqrt(1 -x^2) + sqrt(1 - y^2) = a(x - y) prove that (dy)/(dx) = (sqr...
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- If x = e^(x/y), prove that (dy)/(dx) = (x-y)/(x log x).
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- If y^(x) = e^(y -x), prove that (dy)/(dx) = ((1 + log y)^2)/(log y).
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- If y = (cos x)^((cosx)^((cosx)^(-"to"oo) show that (dy)/(dx) = (cdot...
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- If y = tan^(-1) x find (d^2y)/(dx^2) in terms of y alone.
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