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- If f(x)=x^3+7x-1, then f(x) has a zero between x=0a n dx=1 . The theor...
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- Show that tan^(-1)x > x/(1+(x^2)/3)ifx in (0,oo)dot
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- Consider the function f(x)={xsinpi/x ,forx >0 ,forx=0 The number of ...
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- For x > 0 lf x=pi/2, show that x-(x^3)/6 < sinx < x
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- Let f(x) be a twice differentiable function for all real values of x a...
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- Show that 0 < xsinx-1/2 sin^2x < ((pi-1))/2 ,AAx in (0,pi/2) dot
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- The value of c in Lagranges theorem for the function f(x)=logsinx in t...
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- Prove that ln(1+x) < x for x > 0.
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- If the function f(x)=a x^3+b x^2+11 x-6 satisfies conditions of Rolles...
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- Prove that |cosalpha-cosbeta|lt=|alpha-beta|
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- A value of 'c' for which the conclusion of mean value theorem holds fo...
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- If a , b > 0 a n d 0 < p < 1, then prove that (a+b)^p < a^p+b^pdot
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- Each question has four choices, a,b,c and d, out of which only one is ...
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- Let fa n dg be differentiable on R and suppose f(0)=g(0)a n df^(prime)...
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- The abscissa of the point on the curve sqrt(x y)=a+x the tangent at wh...
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- For 0ltxltpi/ 2, prove that cos(sinx)gtsin(cosx)
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- In which of the following functions is Rolles theorem applicable? (a)f...
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- Show that x/(1+x)ltlog(1+x)ltxforallxgt0.
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- A point on the parabola y^2=18 x at which the ordinate increases at t...
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- Prove that e^x+sqrt(1+e^(2x))geq(1+x)+sqrt(2+2x+x^2)AAx in R
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