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ORDER BY `video_id` desc Continuity and Differentiability 12th Standard CBSE Maths Examine the continuity of the function f (x) = \(\frac { 1 }{ x+3 } , x\ \in \ R\). Give an example of a function which is continuous at x = 1, but not differentiable at x = 1. State the points of discountinuity for the function \(f(x)= [x]\) in \(-3 < x < 3.\) If y= sec-1 \(\left( \frac { \sqrt { x } +1 }{ \sqrt { x } -1 } \right) + sin^{ -1 }\left( \frac { \sqrt { x } -1 }{ \sqrt { x } +1 } \right) ,\ find\frac { dy }{ dx } .\) Differentiate the following w.r.t. x, or find \(\frac { dy }{ dx } \). Find the points in the open interval (0, 3) where the gretest integer function f(x) = [x] is not differentiable Is it true that log (xsinx+cossinx x)=sinxlogx+sin x logcos x? Discusss the continuity of the function f(x) = sin|x| If y = ax +xa+xx+aa, find dy/dx If x = \(\frac { at }{ 1+{ t }^{ 2 } } ,y=\frac { a{ t }^{ 2 } }{ 1+{ t }^{ 2 } } ,find\frac { dy }{ dx } at\) t = 2 \(y={ tan }^{ -1 }\frac { 5x }{ 1-6{ x }^{ 2 } } \),\(-\frac { 1 }{ \sqrt { 6 } } Check the points where the constant function: Find the derivative of tan(2x+3). \(Find\quad f'(x)\quad if\quad f(x)={ \left( sin\quad x \right) }^{ sinx }Taking\quad logs.,\quad log\quad f(x)=sin\quad xlog(sin\quad x)\) For what values of 'a' and 'b', the function 'f' is defined as: For the function \(f\left( x \right) ={ x }^{ 3 }-{ 6x }^{ 2 }+ax+b\), it is given that f(1) = f(3) = 0. Find the values of a and b and hence verify Rolle's Theorem on [1, 3]. For what value of k, is the following function continuous at x=2 ? If a function f is differentiable at a point c, then it is also continuous at that point. Determine the constants a and b, such that the function Differentiare tan-1 \(\left( \frac { acosx-bsinx }{ bcosx+asinx } \right) \) Differentiate \(\left( x+\frac { 1 }{ x } \right) ^{ x }+x^{ \left( x+\frac { 1 }{ x } \right) }\) Find \(\frac { dy }{ dx } \) if \(y=e^{ sin^{ 2 } }x\left\{ 2tan^{ -1 }\sqrt { \frac { 1-x }{ 1+x } } \right\} \)
12th CBSE Mathematics Unit 5 Continuity and Differentiability Important Question Paper
Shalini Sharma - Udaipur Jul-29 , 2019
Continuity and Differentiability Important Questions
Reg.No. :
\(y={ e }^{ x }+{ e }^{ { x }^{ 2 } }+{ e }^{ { x }^{ 3 } }+{ e }^{ { x }^{ 4 } }+{ e }^{ { x }^{ 5 } }.\)
f(x) = k is continuous.
\(f\left( x \right) =\begin{cases} 3ax+b\quad if\quad x<1 \\ 11\quad if\quad x=1 \\ 5ax-2b\quad if\quad x>1 \end{cases}\)is continuous at x = 1.
\(f(x)=\begin{cases} { 2x }+1,\quad if\quad x<2 \\ \quad k\quad\ ,\quad if\quad x=2 \\ 3x-1,\quad if\quad x>2 \end{cases}\)
\(f(x)=\begin{cases} { ax^{ 2 } }+b,\quad if\quad x>2 \\ \quad 2\quad \ \ ,\quad if\quad x=2 \\ 2ax-b,\quad if\quad x<2 \end{cases}\) is continuous.
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