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BANSAL-APPLICATION OF DERIVATIVE-All Questions
- Show that the equation x^5-3x-1=0\ has a unique root in [1,2] .
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- Prove that x/(1+x)>ln(1+x)< x AA x>0
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- f( x )=cos3x−15cosx+8 in [ π/ 3 , 3π/ 2 ] is increasing or ...
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- Use the function f(x)=x^(1/x),x >0, to determine the bigger of the two...
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- Prove that e^x-e^(-x)-2x >0\ AA\ x > 0. Hence, prove that e^x+e^...
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- prove that the function f(x)=(lnx)/x , is strictly decreasing in...
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- Verify Rolles Theorem for f(x)=(sin x)/(e^x)\ in\ [0,pi]\ \ \ \ ...
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- Find c of L M V T f(x)=\ sqrt(x-1)\ \ " in "\ [1,3]
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- Using Lagranges mean value theorem, prove that |cosa-cosb|<=|a-b|dot
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- Verify Rolles theorem for the function f(x)=(x-a)^m(x-b)^n on the inte...
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- Let f(x)=4x^3-3x^2-2x+1, use Rolles theorem to prove that there ...
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- Let f be a twice differentiable function on [0,2] such that f(0)...
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- Find the value of a , if the equation x-sinx=a has a unique r...
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- Find the intervals in which the given function increases or decreas...
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- Prove the following inequalities 1+cotx\ lt=cotx/2\ AA\ x in (0,pi)
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- Leg f(x)=x^3+a x^2+b x+5sin^2x be an increasing function on the set Rd...
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- Find the values of x where f(x)=sin(lnx)-cos(lnx) in strictly increasi...
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- Prove that sin^2theta<thetasin(sintheta)for0<theta<pi/2dot
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- Let f: R->R be a function such that f(x)=a x+3sinx+4cosxdot Then f(x...
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- f(x)=(x-2)|x-3| is monotonically increasing in (a)(-oo,5/2)uu(3,oo)...
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