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BANSAL-LIMITS AND DERIVATIVES-All Questions
- For a positive constant a find (dy)/(dx) , where y=a^(t+1/t) and x=(t+...
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- Differentiate sin^2x w.r.t. e^(cosx) .
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- Find (dy)/(dx) , if y=12(1-cost) , x=10(t-sint)
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- Find (dy)/(dx) , if y=sin^(-1)x+sin^(-1)sqrt(1-x^2) , -1lt=xlt=1
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- If xsqrt(1+y)+ysqrt(1+x)=0, prove that (dy)/(dx)=-1/((x+1)^2)
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- If cosy=xcos(a+y) , with cosa!=+-1 , prove that (dy)/(dx)=(cos^2(a+...
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- If x=a(cost+tsint) and y=a(sint- tcost) , find (d^2y)/(dx^2) .
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- If y=e^acos^((-1)x) , -1lt=xlt=1 , show that (1-x^2) (d^2y)/(dx^2)-x(d...
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- If y=|sinxcosxsinxcosx-sinxcosxx1 1| , find (dy)/(dx) .
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- if =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2)...
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- If (1+x)^n=C0+C1+C2\ x^2+\ dot+Cn\ x^n , using derivatives prove th...
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- If f,g,a n dh are differentiable functions of xa n d(x)=|fgh(xf)'(x...
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- If f(x)=|"cos"(x+x^2)"sin"(x+x^2)-"cos"(x+x^2)"sin"(x-x^2)"cos"(x-x^2...
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- Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...
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- Evaluate ("Lim")(x->0)(xcosx-"ln"(1+x))/(x^2)
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- Evaluate find a and b if \ ("Lim")(x->0)(x(1+acosx)-bsinx)/(x^3)=1
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- ("Lim")(x->0)(e^xsinx-x-x^2)/(x^2+x-"ln"(1-x))
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- Evaluate: ("Lim")(x->0)(1+sinx-cosx+"ln"(1-x))/(xtan^2x) -1/2 (b)...
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- Evaluate: ("Lim")(x->0)((log)(secx/2)(cosx))/((log)(secx)(cos(x//2))) ...
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- Evaluate: ("Lim")(x->1)(x^x-x)/(x-1-lnx)
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