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				   if f(x) = { 3-x2 , -1[_x[_2
{ 2x-4 ,  2[_x[_4 then find fof(x)and discuss the continuty and differentiability


4 years ago

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										Ans:$f(x) = \left \{ 3-x^{2}, -1\leq x< 2 \right \}$$f(x) = \left \{ 2x-4, 2\leq x\leq 4 \right \}$Continuity,Left Hand Limit(LHL) = Right Hand Limit(RHL) = f(2)$LHL = \lim_{x\rightarrow 2^{-}}3-x^{2} = -1$$RHL = \lim_{x\rightarrow 2^{+}}2x-4 = 1$$LHL\neq RHL$f(x) is not continuous at x = 2Similarly you can find Left Hand Derivetive & Right Hand Derivative$LHD=\lim_{x\rightarrow 2^{-}}\frac{f(x+2)-f(2)}{x}$$RHD=\lim_{x\rightarrow 2^{+}}\frac{f(x+2)-f(2)}{x}$f(x) is not differentiable at x = 2Thanks & RegardsJitender SinghIIT DelhiaskIITians Faculty

one year ago

What is the minimum and maximum value of the function x/(ln(x!))?Please explain the answer.

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 Vijay Mukati 10 months ago
best book for calculus for iit and school 1)sk goyal 2)amit m agrwal

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 vivek 7 months ago
The equation of the common tangent to the equal parabola y^2=4ax and x^2=4ay is?

The tangent on y^2 = 4ax will be y = mx + a/m Since this lines touches the x^2 = 4ay. Therefore replace y here by y = mx + a/m and simplify, You will get the quadratic in x. Now since this...

 Vijay Mukati 5 months ago
Consider the equation ; x 4 + ax 3 - 6x 2 + ax + 1 find parameter of a for which equation has two distict positive roots ?

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 Akshay 10 months ago

The answer is a is (-infinity,2). Consider only positive side of x-axis for analysis, that is x>0. At a=2, you get f(x)=x 4 +2x 3 -6x 2 +2x+1, Differentiating with respect to x: f’(x)=4x 3...

 Akshay 10 months ago

When a(is less than)2, {f(x) when a(is less than)2} (is less than) {f(x) when a=2}. At x=1, you will get f(x)(is less than)0. As f(0)(is less than)0 and f(infinity)>0 , you will get two...

 Akshay 10 months ago
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