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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
- Find (d^2y)/(dx^2) when y = e^x sin x
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- Find (d^2y)/(dx^2) when y = x^2 + tan x
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- Find (d^2y)/(dx^2) when y = x^3 + tan x
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- Find the second derivative of log x + cosx.
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- If y = tan x + sec x, prove that (d^2y)/(dx^2) = (cosx)/((1-sinx)^2)
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- If y=log (x+ sqrt ( x^2+1)), prove that: (x^2+1) d^2y/dx^2 + xdy/dx=0.
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- Find the second order derivative of e^(x tanx)
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- If y = tan^-1 x , find (d^2y)/(dx^2) in terms of y alone.
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- If y = A sinx + B cosxthen prove that d^2y/dx^2 + y = 0
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- If y = 3 cos (log x) + 4 sin (log x) show that x^2 y2 + xy1 + y = 0
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- If y = Ae^(mx) + Be^(nx), Show that (d^2 /dx^2 y)-(m+n)dy/dx+mny = 0
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- If y=e^(ax)cosbx, then prove that (d^(2)y)/(dx^(2))-2a(dy)/(dx)+(a^(2)...
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- If y = (sqrt(x+1) - sqrt(x-1)), then prove that (x^2-1) y2 +xy1 = 1/4 ...
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- y = e^(m sin^(-1)x), prove that (1 - x^2) y2 - xy1 = m^2y
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- If x^2/a^2 - y^2/b^2 = 1, prove that ((d^2y)/dx^2) = (-b^4)/(a^2y^3)
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- If (x-a)^2 + (y-b)^2 = c^2 , for some c > 0, prove that [1+(dy/dx)^2]...
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- Find (d^2y)/dx^2, if x = a (theta - sin theta), y = a(1+cos theta)
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- If x = 2 cos theta - cos 2 theta, y = 2 sin theta - sin 2 theta, find ...
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- If x = a { cos t + log|tan t/2|} and y = a sin t, 0 < t < pi/2, find (...
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- If x=acos theta+bsintheta and y=a sintheta-bcostheta, then prove that ...
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