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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


3 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

attachement is not visible, please write the quesion on forum , otherwise not possible to help you.

=5 +n/1 + n(n-1) / 2! + ….....+ n!/n! next step I want to understand (1+1)^n + 4 = 2^n + 4

 milind one year ago
find the equation of a line passing through the point 3,2 and perpendicular to the line x=y

the line is y=5-x since the line is perpendicular to line y=x, the slope of this line is -1. and acc. to point slope formula i.e., (y-y’)=m(x-x’) hence (y-2)=(-1)(x-3) y-2=3-x y=5-x

 Avani Patidar 28 days ago
Pl provide soln to the attached image!!

a n = Limit x 2 *(f(a n-1 /x) – f(0)) 2 , a n /a n-1 2 = Limit [ [ f(a n-1 /x) – f(0) ]/[ a n-1 /x – 0] ] 2 a n /x will be tendind to 0 as x tends to inf. hence RHS = f’(0) 2 So, an/an-1^2...

 Akshay one month ago
2 PLUS 2

 A M S ARUN KRISHNA 29 days ago

4

 noogler 29 days ago
The equation of common tangent of the parabolas y^2=32x and x^2=108y

first write the equation of tan gent in slope form for both the parabolas i.e y=mx+a/m -1 and x=my+a/m -2 now compare the cofficients of x,y,m,a get the value of m and put in and get the...

 ashu one month ago
what is the antiderivative of sinx

anti derivative means integration and its value equals theta1 theta2 ∫sinx.dx = -cos(theta1-theta2) +c approve if useful

-COSX

 noogler 3 months ago
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