Recently Active Calculus Questions

\text{For x} >0,lim_{x\to 0}\left(\left(sinx\right)^{\frac{1}{x}}+\left(\frac{1}{x}\right)^{sinx}\right) \ is ...

ƒ : R → R is a twice diffentiable fn. such that ƒ'(x) = ƒ(1-x) for all x \epsilon R Given ƒ(0) = 1 , Find ƒ(1) (A) e - 2 (B) ln 2 - 1 (C) sec 1 + tan 1 (D) cos 1 + sin 1 ...

is this a DONKEY's toil - work Question Or has some more Elegant - Plausible Approach to it ?? [7] *Image* ...

There are exactly 2 distinct linear functions which map [-1,1] onto [0,2].Find them. ...

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The rate of change of a double ordinate of x2=4by is proportional to its length,if the ordinate is varied frm the vertex,then the area traversed in time (ln4)/3k is ? (k is prop const) ...

integration sikho and sikhao people this riddle is for u : Lets try to out-riddle this riddle , Evaluate Walli's formula using βετα function . ...

is y=xtan(1/x) continuous at x=0?? easy one I know but My answer is not matchimg ...

must see for all people intrested in solving riddle : Let me see if u can solve this riddle , solve this limit and prove ur mettle . lim (n!/nn){(2n4+1)/(5n5+1)} n→∞ ...

(1+y2)dx=(etan-1x-x)dy ...

\lim_{x\rightarrow 0} \frac{2Sin3x-Sin6x}{x^3} By LHospital i am getting -27 But by another method i am getting 0 the other method is \lim_{x\rightarrow 0} \frac{2Sin3x}{x^3}-\frac{Sin6x}{x^3} \lim_{x\rightarrow 0} \frac{2*3S ...

find the condition on \lambda such that this eqn has real roots f(x) = \sqrt{3}\lambda x^4 - x^3 + 3\sqrt{3}\lambda According to the descartes rule,this eqn has either 2 or 0 roots,but i'm not getting any further frm here ...

\int_{0}^{\pi/3 }{(f'(3x)+f'''(3x))}cos3xdx=-5 find f"(0) +f"(\pi ) ...

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7. If f(x) is a monotonic differentiable function on [α, β] then αβ∫f(x)dx + f(α)f(β)∫f-1xdx equals to (A) β f (β) – α f (α) (B) β f (α) – α f (β) (C) α f (α) + β f (β) (D) none of these ...

Let f be twice diff function satisfying f(1)=1,f(2)=4,f(3)=9 then: a)f"(x)=2 b)f'(x)=2 c)there exists at least one x E (1,3) such that f ' (x)=2 ...

FIND da area bound by the curves : y = x2 + 2 & y = 2|x| - cos(Î x) OPTIONS : 2/3 4/3 8/3 1/3 ...

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What are the points of discontinuity of f(x)=[x]+\{x\}^{[x]}\qquad \forall \ x\ge \dfrac{1}{2} Here [x] is the greatest integer function, and {x} is the fractional part of x. ...

What normal to curve y=x2 forms shortest chord????? ...

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*Image* g(x)= x2 , if x is rationaal = 0 if x is irrational then 1. *Image* 2. *Image* 3. *Image* 4. *Image* ...

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At what points is the function f(x)=[x^2]\sin \pi x\qquad \forall\ x\in\mathbb{R} discontinuous? ...

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let f:(2,4)→(1,3) f(x)= x - [x/2] f-1(x) = ...

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