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- Let f(x)=x^3-3x^2+6AAx in \mathbb{R} and g(x)={m a x :f(t ; x+1lt=tlt=...
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- From a fixed point A on the circumference of a circle of radius r , th...
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- The lower corner of a leaf in a book is folded over so as to reach the...
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- h(x)=3f((x^2)/3)+f(3-x^2)AAx in (-3, 4) where f''(x)> 0 AA x in (-3,4)...
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- If 0<x1<x2<x3<pi, then prove that sin((x1+x2+x3)/3)>(sinx1+sinx2+sinx3...
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- Prove: sin^2θ+cos^2θ=1
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- Prove that (tan^(-1) 1/e)^2+(2e)/ sqrt(e^2+1)<(tan^(-1)e)^2+2/(sqrt(e^...
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- If f(x)=x^3+bx^2+cx+d and 0ltb^2ltc then in (-oo,oo)
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- The function defined by f(x)=(x+2)e^(-x) is (a)decreasing for all x ...
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- Find the values of x where f(x)=sin(lnx)-cos(lnx) in strictly increasi...
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- Let 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 possible values of a such that f(x)=e^(2x)-(a+1)e^x+2x is mon...
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- Prove that for any two numbers x1 and x2.(2e^(x1)+e^(x2))/3gte^((2(x1)...
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- Assertion Consider the following statements in SandR S: Both sinx and...
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- Let f(x)=int0^xe^t(t-1)(t-2)dt, Then f decreases in the interval
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- The length of the longest interval in which the function 3sinx-4sin^3x...
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- Tangent is drawn to ellipse (x^2)/(27)+y^2=1 at (3sqrt(3)costheta,sint...
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- If f(x)=xe^(x(1-x)) , then f(x) is(a) increasing on [−1/2,1] (b) decr...
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- Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x) as b...
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- Suppose that f is a polynomial of degree 3 and that f^(x)!=0 at any...
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